Program Gibbs. Tutorial Part B. Frank S. Spear by Frank S. Spear

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1 Program Gibbs Tutorial Part B by Frank S. Spear 2001 by Frank S. Spear

2 F. S. Spear Program Gibbs Tutorial 34 Program Gibbs Tutorial Part B Differential Thermodynamics The Gibbs Method Feb, 2001 Frank S. Spear Department of Geology, Rensselaer Polytechnic Institute, Troy, New York spearf@rpi.edu Table of Contents Introduction Starting the program The Main Menu Exercise 1: Analysis of a garnet-grade schist Introduction Geologic setting Petrography Mineral composition and zoning Exercise 1.A. Thermobarometry Exercise 1.B Contouring divariant regions Exercise 1.C P-T paths from zoned garnet Exercise 1.D Forward modeling of garnet growth Exercise 2: P-T paths calculated from zoned garnet: The Tauern Window Appendix 1. PostScript graphics files... 59

3 F. S. Spear Program Gibbs Tutorial 35 Program Gibbs Tutorial Part B Differential Thermodynamics Introduction Program Gibbs has two main calculation modes integrated (Newton s method) and differential (Gibbs method) thermodynamics. Differential thermodynamics mode is designed to calculate changes in dependent thermodynamic variables given user-specified changes in independent variables. The choice of which variables are independent is up to the user, making this a very powerful algorithm for calculating useful petrologic diagrams. It is important to recognize that virtually all of the types of calculations that can be done using differential thermodynamics can also be done using the integrated mode. The only catch is that consistent enthalpies and solution models are required for integrated mode calculations, and these are not available for all phases. The differential mode is useful, therefore, in the analysis of real rocks where the full complexity of the chemical system is to be considered. Examples of useful calculations to do with differential thermodynamics include 1) Contouring P-T diagrams for mineral composition and modes; 2) Forward modeling of garnet zoning 3) Inverse modeling of P-T paths from garnet zoning 4) Whole-rock reaction balancing There is a philosophical difference in how to view a rock between the differential and integrated approaches. The integral approach starts with the end-member thermodynamic data and activity models and attempts to calculate the mineralogy and mineral composition of the rock under study. In a way, the petrologist attempts to force the rock into its proper thermodynamic cubbyhole. The differential approach starts with the question what changes caused this rock to be? That is, what changes in P and T (i.e. independent variables) produced the observed reaction textures and mineral zoning? In the differential approach we start at a point near the metamorphic peak and attempt to work backwards. This section provides step-by-step instructions for these specific types of calculations. Where possible, an attempt will be made to integrate the calculations into realworld examples so that the reader can gain an appreciation of the types of problems that can be solved with differential thermodynamics. Starting the program When you start program Gibbs you will see a splash screen with an image of the program s namesake. You will then be asked to select a thermodynamic data file from a list. Thermodynamic data files in Gibbs.fig file: 1 Gibbs Tutorial Thermo.dat

4 F. S. Spear Program Gibbs Tutorial 36 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 Choose the Gibbs Tutorial Thermo.dat file. Note that the Gibbs Tutorial Thermo.dat file can be used only in differential thermodynamics mode. HoPo Thermo, S&C, and SPaC can be used in differential or integral 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 = 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 = Go to global menu 9 = Plotting menu 10 = Plot digitized reactions 11 = Thermodynamic data menu CHOOSE OPTION It is first necessary to open a Gibbs input file. In integrated mode (Tutorial- Part A), it was generally easiest to select minerals from the master input files. Since we are calculating the equilibrium compositions anyway, it doesn t matter that the input minerals aren t exactly the correct compositions. In differential mode, we generally open a file that contains the compositions that we believe represent an equilibrium assemblage at some T and P. These data are obtained from analysis of mineral compositions using the electron microprobe. It is very important that the mineral compositions are chosen carefully because the program will take these as the reference compositions. In effect, this establishes the H of reaction for every independent reaction in the system (although the H values are never explicitly calculated). Input files can be constructed using any text editor. Also, there is a routine in Gibbs to help construct an input file from natural data (see Appendix for details).

5 F. S. Spear Program Gibbs Tutorial 37 Exercise 1: Analysis of a garnet-grade schist Introduction As a means of introducing the calculation possibilities of Program Gibbs, as well as the philosophy behind these calculations, this first exercise will focus on analysis of a garnet-grade schist from southwestern New Hampshire. Geologic setting The sample to be examined (PUT92-C2) comes from a garnet-grade schist from the Devonian Littleton Formation in eastern Vermont. The region is characterized by westvergent fold and thrust nappes with later doming. The over all metamorphic gradient across this region is inverted with the higher grade metamorphic rocks located in the structurally highest nappes. Sample PUT92 comes from one of the lowest nappes and the P-T history of the sample has been influenced by higher level nappe emplacement. N ME ML JR VT NH MA CT RI Area of map EVB OB MD Co Co Green Mtns CD JR CYL BHB BG Co MB Co AthD FM KQM Co PUT92 AD KD Co Co Explanation Mesozoic basin rocks JR White Mountain magma series Co Co N. H. and central Mass. Concord Granite series New Hampshire magma series MA VT Co NH Co MA Ord - Sil - Dev cover rocks Oliverian and dome gneisses Vt. and western Mass. Connecticut Valley sequence Late pc - C - Ord rocks pc of Green Mountains and domes Scale (km)

6 F. S. Spear Program Gibbs Tutorial 38 Petrography The assemblage in sample PUT92-C2 is garnet + biotite + chlorite + muscovite + plagioclase + quartz + ilmenite. Garnet is subhedral and the core contains inclusions of an earlier foliation that is orient roughly the same as the matrix foliation. The dominant foliation is believed to have formed during formation of early recumbent folds, and this texture indicates that garnet grew predominantly following foliation formation. Minor flattening of the foliation around garnets suggests that there was some reactivation of the foliation during thrust emplacement. Minor retrogression is observed around the rim of garnet in the form of late chlorite replacement. The effect of this late ReNTR (retrograde net transfer reaction) on thermobarometry will be discussed below.

7 F. S. Spear Program Gibbs Tutorial 39 Mineral compositions and zoning Garnet from sample PUT92-C2 is zoned with typical garnet-grade zonation. Fe Mg Fe, Mg and Mn zoning in garnet, sample PUT-92C2, Putney, Vermont. The zoning is typical of prograde growth zonation by the reaction chlorite + quartz = garnet + H 2 O. Core-rim zoning are: Alm: Prp: Sps: Grs: We will use the Gibbs Program to determine over what P-T paths this type of zoning is possible. Click on an image to load TIFF file into NIH Image. Mn

8 F. S. Spear Program Gibbs Tutorial 40 Ca zoning decreases from Xgross = 0.17 in the core to on the rim. The change in grossular content is, in part, a function of changing P-T conditions, and, in part, a function of Rayleigh fractionation. The only other Ca-bearing phase in this sample is plagioclase, and growth of garnet requires consumption of anorthite component of plagioclase. As can be seen below, plagioclase is zoned towards more albitic rims. Ca Plg This close view of plagioclase zoning shows the core-rim relations. The maximum core An content is An(40) and the minimum rim content is An(04). Note the irregular (non radial) zoning. This is because plagioclase doesn t homogenize by diffusion, and consumption of plagioclase during garnet growth is not necessarily radial.

9 F. S. Spear Program Gibbs Tutorial PUT-92 C Alm Sps Grs Prp Line traverse across garnet plotted in Excel from data in X-ray map.

10 F. S. Spear Program Gibbs Tutorial 42 Trace element zoning in garnet Yttrium in garnet (upper image) can be a sensitive monitor of temperature of garnet growth and reaction history, especially when xenotime is present in the sample. This garnet has a high Y core (1900 ppm), a zone of lower Y and a higher rim. The very upper left margin of the top crystal has a high Y rim. Sc (left) increases outward from core and then decreases again to the rim

11 F. S. Spear Program Gibbs Tutorial 43 Exercise 1.A Thermobarometry The peak metamorphic temperature of this sample can be inferred from examination of a petrogenetic grid to be on the order of C. Fe-Mg exchange thermometry has a resolving power of ±25 C, so it is not likely that this estimate can be improved upon greatly. Peak pressure, on the other hand, is not constrained at all by the phase assemblage, and geobarometry is very useful for inferring the crustal thickness at the time of metamorphism. There are two general approaches to thermobarometry currently in practice. Independently calibrated thermobarometers are equilibria for which a calibration of the temperature and pressure dependence of the equilibrium constant has been published. Individual equilibrium relations may have several different published calibrations. For example there are over ten calibrations of the garnet-biotite Fe-Mg exchange thermometer. Program GTB has been coded to incorporate most of the published thermobarometers useful for metamorphic rocks. Internally consistent thermobarometers utilize all independent equilibria in a metamorphic assemblage and plot them all on a P-T diagram. If the sample is wellequilibrated, the thermodynamic data set is internally consistent, and activity models are accurate, then all curves should intersect at a point in P-T space. The degree to which curves do not intersect at a point is a measure of the degree of disequilibrium, inconsistency of thermodynamic data, or inaccuracy of activity models. Programs Thermocalc (Holland and Powell) and TWQ (Berman) are designed to perform these calculations. Program Gibbs can also perform these calculations, but currently there is no simply way to translate measured mineral compositions into activity models consistent with the thermodynamic data bases. Two Fe-Mg exchange thermometers (garnet-biotite and garnet-chlorite) and one garnet-plagioclase barometer (garnet-plagioclase-muscovite-biotite) apply to sample PUT92-C2. We will demonstrate the use of program GTB with these thermobarometers. Garnet-biotite thermometry 1) Start program GTB 2) Open mineral file PUT 92C2.asm (option 1) you will see a listing of key words in the file. Hit return 3) Choose option 3 (plot Keq lines) 4) Once in the thermometer menu, choose option 1 (Grt-Bt), then choose the Hodges and Spear calibration (#2). Do not correct for Fe3+ (option 0) 5) You now proceed to choose Grt-Bt pairs, one at a time. To choose a mineral, highlight the specific analysis, and either double click, or click OK. Garnet will be chosen first, then biotite, and after the selection of biotite, a KEq line will be plotted on the P-T diagram. Choose these pairs a) Grt 5 + Bt 16 b) Grt 5 + Bt 17 c) Grt 5 + Bt 28 d) Grt 5 + Bt 29 e) Grt 5 + Bt 30 f) Grt 5 + Bt 31 The keys next to the mineral analyses indicate the textural position of the analysis. For example, "chl_rim_grt" is a chlorite in contact with a garnet rim, "mtrx_chl", is a matrix chlorite, etc. For this exercise, plot garnet analysis 5 (rim of garnet against all biotites

12 F. S. Spear Program Gibbs Tutorial 44 6) Once done selecting Grt-Bt pairs, select cancel, and then select option 0 (return to Rxn Menu) 7) Choose option -1 (Next Menu). This will bring up the geobarometer menu 8) Choose barometer 2 (Grt-Pl-Ms-Bt) 9) Choose the Hodges and Crowley calibration (option 3) 10) In the same manner as before, select Grt-Pl-Bt-Ms pairs. For this exercise, select rim garnet (5), a single matrix biotite (28) and muscovite (27), and pair these with all plagioclase analyses (33, 34, 35,36,37,38), as we are interested in pressure variation, which is indicated by variations in grossular content of garnet and anorthite content of plagioclase. The results should look like the diagram on the left. 10 Discussion The small range of garnet-biotite temperatures and garnet-plagioclase-muscovitebiotite pressures suggests that the matrix of the sample is well-equilibrated. Although the chlorite on the rim of the garnet suggests there is some of retrograde hydration, it does not seem to have affected the biotite compositions, inasmuch as the biotite touching the garnet gives the same temperature as the matrix biotite far from the garnet rim. PUT-92C2 Rim thermobarometry 10 PUT92-C2 Grt-Chl thermometry P kbar Grt-Bt Grt-Plg-Bt-Ms P kbar Grt rim + matrix Chl Grt rim + retro Chl T C T C Garnet-chlorite thermometry Repeat the above exercise using garnet (5) + every chlorite. Chlorites numbered 14, 15, 18, and 20 are the retrograde chlorites touching the garnet rim and chlorites 21, 22 and 26 are in the matrix away from the rim. The chlorites that are touching garnet give a higher temperature than the chlorites in the matrix because they were produced by a retrograde net transfer reaction (ReNTR). The reaction probably only operated very locally (right on the rim of the garnet) because there are no late, crosscutting chlorites in the matrix. In some samples, pervasive operation of ReNTRs can result in production not only of Fe-rich chlorite, but also Fe-rich biotite (biotite maintains exchange equilibrium with chlorite during retrogression). If this had happened, then garnet-biotite Fe-Mg exchange thermometry would have yielded a temperature above the metamorphic peak.

13 F. S. Spear Program Gibbs Tutorial 45 YAG-xenotime and YAG-monazite thermometry Recently calibrated YAG-xenotime (Pyle and Spear, 2000) and YAG-monazite (Pyle et al., in press) thermometers have been applied to the sample. Application of the YAG-Xno thermometer to the core (1902 ppm Y) yields a temperature estimate of 497 C. This estimate is a maximum, as xenotime was not observed in the sample. Application of the YAG-monazite thermometer, using rim compositions of garnet, plagioclase, monazite, and assuming an X OH-Ap of 0.1 yields a temperature estimate of 496 C. The garnetmonazite temperature is consistent with the temperatures obtained from garnet-biotite and garnet-chlorite Fe-Mg exchange. The garnet-xenotime temperature from the garnet core might suggest little temperature change during garnet growth, but this temperature is a maximum because xenotime was not observed in the garnet core. P-T path calculations discussed below suggest that the core of the garnet nucleated at approximately 450 C [Y] Grt vs. T Xenotime-bearing samples 10 YAG+OH Ap+Qtz=Grs+AN+Mnz+W Monazite-bearing samples 4000 : σ Y = 100 ppm : σ T based on σ Y 8 PUT 92C2 KEq =0.4 ppm Y in garnet PUT 92C2 Grt Core: 1902 ppm Y (maximum T) P Kbar Tmax YAG-Xno YAG-Mnz T estimate, Grt rim + matrix Mnz T ( C) T ( C)

14 F. S. Spear Program Gibbs Tutorial 46 Exercise 1.B Contouring divariant regions using differential thermodynamics (Gibbs method) with mass balance constraints A useful application of the Gibbs Program to understanding this sample is to construct a contour diagram that shows how mineral composition and modal mineralogy changes with P and T. For this purpose we will use differential mode and the compositions on the rim of the garnet as reference conditions. These compositions have been stored in a Gibbs input file named PUT92C2_Gibbs.in. We will draw contours for garnet and plagioclase compositions that reflect both the rim and core compositions, as listed in the table below: Put92-C2. Garnet and plagioclase rim and core compositions Plagioclase Garnet Xan Xprp Xalm Xsps Xgrs Fe/(Fe+Mg) Rim Core ) Start Program Gibbs 2) Select the Gibbs Tutorial thermo.dat file 3) From the Gibbs main menu, select Begin/Save new problem a) Select 1 (Open Gibbs input file) b) Open the file PUT92C2_Gibbs.in c) Type 0 to return to the main menu 4) From the main menu, select 3 (Contour x-y plots) We will use the Absolute contour routine to make the contour diagram. The procedure will be as follows: 5) From the Contour menu, select 3 (Absolute contour routine) a) Select the variable to contour start with Xalmandine b) Click Reset c) Click Select d) Type in the value to contour (the rim composition first) e) Click Compute contour If the program beeps, just hit return f) Type in the core value to contour g) Click Compute contour h) Click Cancel to exit the routine 6) Now reset the data to the starting conditions (rim compositions). To do this: a) Select 6 (Reference Points) b) Select 3 (Return to start) 7) Now repeat 5-16 for each of the composition variables in the table. Do spessartine last (this requires some special handling) 8) To contour spessartine: You will discover when you try to contour spessartine at the core composition that the program can t find the contour. This is because the contour curves back on itself and doesn t have a solution at P = 6 kbar. If we know this is what is happening, we can help the program along in the following way. a) After resetting to the starting conditions, select 5 (Move to a new contour). This will bring you to the Steps menu b) Select 2 (Choose monitors) i) Click Reset and select T and P as monitors ii) Type in 3000 for P. This will decrease P from 6000 to 3000 bars at constant temperature.

15 F. S. Spear Program Gibbs Tutorial 47 iii) Type in 30 for Number of finite difference iterations (100 bar steps). iv) Click Done c) From the steps menu, select 4 (Compute one increment). This will lower the pressure at constant temperature. d) Select 0 (return). This will bring you back to the contour menu e) Now continue contouring Spessartine. Select 2, specify the spessartine contour and compute. The program should be able to find the core spessartine contour at P = 3000 bars. 9) If you wish, you can also contour moles of garnet. Repeat 5-16 and on 6, select Mgarnet. Type in the value of moles of garnet at the rim and compute the contour. Now type in 0.0 moles (the garnet isograd) and click compute. It probably won t work using this routine because 10) When you are done, you can save the file if you wish. The final result, after some cleaning up in Illustrator, looks like this: Prp Sps Prp PUT92-C2 (+ mass balance) 7 P kbar Sps 0.22 MGrt Alm 0.59 MGrt An Grs 0.17 An 0.40 Grs Fe/(Fe+Mg) Alm 0.84 Fe/(Fe+Mg) T (C) P-T contour diagram for sample PUT92-C2. Each color is a different contour. Solid lines are rim contours, dashed lines are core contours.

16 F. S. Spear Program Gibbs Tutorial 48 Discussion The contour diagram is useful to help understand how this garnet-zone schist will react along different P-T paths. The rim contours all intersect at a point as they must, because this is the reference conditions. The cyan contours (Mgrt) show that a wide range of P-T paths will produce garnet, including isothermal loading, isobaric heating, and heating with decompression. Ideally, this type of diagram could be used to infer the P-T path during garnet growth, but this doesn t work quantitatively because the diagram is drawn at constant bulk composition, but the rock changes effective bulk composition as it evolves due to fractionation into garnet (e.g. Mn and Ca). Examination of the core contours reveals that there is no P-T region in which they all intersect, as there should be if the diagram was a perfect model for the evolution of this rock. In fact, the region subtended by the garnet core compositions, shown as a purple region, is rather large. Because Mn and Ca are two elements that fractionate extensively into garnet, it is probable that these contours are most affected by the changing bulk composition. If we weight more heavily the core contour for Fe/(Fe+Mg), then the P-T path appears to involve a bit of heating (10-15 C) and possibly some loading. Exercise 1.C P-T paths from zoned garnet (Spear and Selverstone, 1983) A method was developed in the early 1980 s to calculate the P-T path that would produce a measured zoning profile in a garnet. This is the inverse of the contour method shown above because now we will use the changes in composition along the zoning profile as input and compute changes in P and T. It is easy to do this in Program Gibbs because the user has complete freedom over which variables are chosen to be independent. For this exercise, we will choose the garnet and plagioclase compositions to be independent and P and T to be dependent. For this exercise we will not use mass balance constraints. This will result in an increase in the variance of the system of equations from two (Duhem s theorem) to the phase rule variance (four in this example). Therefore, we will need four independent variables to calculate the P-T path. Garnet contains three independent composition variables (we use Alm, Sps, and Grs) and plagioclase contains one (we use anorthite). These are also a good choice because, as we saw in the contour diagram, there is a high angle of intersection between these contours, so changes in both P and T will not be subjects of low angle intersections. The compositions we will use are in the table below. Note that the rim is not exactly the same as specified above, but this is well within analytical uncertainty. Only the core and rim compositions are listed. The numbers we will need for this calculation are the changes in composition from rim to core, which are listed as the increments numbered 1-5. Put92-C2. Garnet and plagioclase zoning for P-T path calculation Plagioclase Garnet An Alm Sps Grs Rim Core

17 F. S. Spear Program Gibbs Tutorial 49 1) Start program Gibbs 2) Choose the Gibbs Tutorial thermodynamic data set 3) Select Begin/Save from the main menu 4) Select 1 (Open input file) and open the file named PUT92C2_Gibbs(noMB).in 5) Select 0 to return to main menu 6) Select 2 (Single Steps) 7) From the Steps menu, select 2 (Choose monitors/set deltas) a) Click Reset b) Select as monitors X An, X Alm, X Sp s, and X Grs. c) Type in the values for the first step (0.05, , ) d) Set Number of Finite difference steps to 10 e) Click Done 8) Select 4 from the Steps menu (Compute). You should see a segment of the P-T path drawn. 9) Repeat 6-8 for each of the 5 steps in the table PUT92-C2 8 Garnet zoning P-T path 7 P kbar Core Rim T (C) Discussion The calculated P-T path shows approximately 50 degrees of heating and 1.5 kbar of loading. Comparison with the contour diagram reveals that the contour diagram gives a good first approximation to the path, although the path calculated directly from the garnet zoning is much more precise. The calculated T is most sensitive to zoning of Fe, Mg and Mn and the calculated change in pressure is most sensitive to the grossular and plagioclase zoning. In the calculation above, it was assumed that the An content of plagioclase changed from 0.15 on the rim to 0.40 in the core. It is always a good idea to examine the sensitivity of the calculated P-T path to uncertainty in the plagioclase composition because it is generally not simple to correlate the core of the garnet with a specific plagioclase composition. Calculating the path using a range of assumptions permits ready evaluation of this sensitivity.

18 F. S. Spear Program Gibbs Tutorial 50 It should be noted that the placement of the path in P-T space is more uncertain than the P and T along the path. Garnet-biotite thermometry has a resolution of approximately ±25 C, but the T of the path is precise to approximately 3-8 C (cf. Kohn, 1993, CMP). Exercise 1.D Forward modeling of garnet growth As a final exercise on this sample, it is useful to attempt to model the observed zoning by forward modeling. In this example, we start at the conditions of the garnet core, and grow garnet along the inferred P-T path, calculating the zoning profile as we go. The final zoning profile can then be compared with the observed profile to see if we have a good match. In more sophisticated modeling, simultaneous diffusion and growth can be simulated to account for homogenization of garnet by diffusion. Interested readers should refer to the DiffGibbs manual for instructions. The initial conditions in the forward model of sample PUT92-C2 are those of the garnet core. We can measure the core composition, but the compositions of other phases in equilibrium with the core are not known (above we assumed that the plagioclase core was also in equilibrium with the garnet core). Our inverse modeling of the garnet zoning profile in Exercise 1.C results in calculating the values of all dependent variables at the garnet core, and we can use these compositions as our initial conditions for the forward modeling. The easiest way to save the results at the garnet core is to use option 5 (Save current problem) from the Begin/Save menu. This has been done and the input file is named PUT92C2_Gibbs_Core.in. We will use the Grow Grt module for this exercise, although we could also use the DiffGibbs module. There are some idiosyncrasies in how the input files must be organized for these two routines. For the Grow Garnet routine, garnet must be the last mineral, and New Variables must bet turned on for garnet only. I ll try to clean them up in the future. Also, it is in principle possible to do these calculations using Newton s method, but I think the code will balk if you try at this point. So the Grow Garnet routine forces you to use the Gibbs Tutorial data set and differential thermodynamics. 1) Start Program Gibbs 2) Select Gibbs Tutorial thermodynamic data file 3) From the main menu, select 5 (Grow Garnet) 4) From the Grow Garnet menu, Select 1 (Open problem/add grt/draw plot) a) Select 1 (Open new input file) and select the file named PUT92C2_Gibbs_Core.in b) Select 3 (draw axes) to redraw the plot c) Select 4 (Pick variables to plot). Type in 1 for each element it requests (this will plot each one) d) You can set the way new garnet is distributed to multiple garnets that nucleate sequentially using option 5. Since we are only modeling a single garnet, this is irrelevant here. e) Select 0 (return) 5) From the Grow Garnet menu, select 2 (Choose monitors). a) Select T and P (if not already selected) b) Type in for T = 50 and P = 500. This will get us to the rim conditions along a linear P-T path. You can, of course, select any P-T path you desire. c) Set Number of finite difference steps to 100 (1/2 degree/step) d) Click Done 6) From the Grow Garnet menu, select 4 (Compute one increment). The garnet zoning profile should show on the screen.

19 F. S. Spear Program Gibbs Tutorial PUT92-C2 Mole fraction Alm Sps Grs Prp Radius (µm) Discussion The model (shown with black lines) is a good match for the data (colored symbols), lending support to the proposed P-T path. Of course, this result is to be expected, because we used the observed zoning profile to calculate the path in the first place. The one exception is grossular towards the rim, where the model calculation is slightly higher than the observed. This is most likely due to the amount of plagioclase that is reacting with the garnet as the reaction proceeds. The input model has 10 modal percent plagioclase, and it is assumed that this plagioclase remains homogenous throughout (despite the observation that the plagioclase is zoned). If the amount of plagioclase involved in the reaction decreases with time, then the grossular in garnet will decrease more than with the homogeneous plagioclase model, consistent with the observed zoning trend. The literature contains discussions about whether the bell shaped Mn profile is due to Rayleigh fractionation, or P-T-X phase equilibrium constraints. A way to evaluate this question is to construct two forward models, one assuming fractional crystallization and one not. An input file similar to the one used above, but with fractional crystallization turned off, is included (PUT92C2_Gibbs_Core(noFx).in). The interested student can rerun the previous exercise with this input file (don t replot the axes because this will erase the screen). The resulting plot looks like this:

20 F. S. Spear Program Gibbs Tutorial PUT92-C2 Fe/(Fe+Mg) Mole Fraction Alm Sps Grs with fractional crystallization (black) No fractional crystallization Prp Radius (µm) Fractional crystallization results in a decrease the radius of the garnet, and a decrease in the rim composition of Mn and Ca and an increase in the rim composition of Fe, relative to the no fractionation model. Of course, without fractional crystallization, garnet would be homogeneous throughout its growth, so a zoned garnet would not actually be produced. The zoning profile shown in red above is actually the trace of the homogeneous garnet composition as it grows.

21 F. S. Spear Program Gibbs Tutorial 53 RG Basel Ivrea Exercise 2: P-T paths calculated from zoned garnet: The Tauern Window One of the first published P-T path calculated using the Gibbs method was for a garnet from the Tauern Window by Selverstone et al. (1984, J. Petrol., v. 25, pp ). At the time this path was calculated, the idea that Barrovian metamorphism typically followed clockwise P-T paths was relatively new. Furthermore, no P-T path had ever been calculated from a natural sample that BM München displayed a clockwise path. Zürich Innsbruck TW P L Helvetic, Flysch, and Penninic Units Australoalpine Units Southern Alps Wien The sample studied by Selverstone et al. (1984) came from a unit called the Lower Schieferhulle series in the southwest Tauern Window, Austria. This unit is part of the Pennine basement and sits with tectonic contacts between the Zentralgneis core and the Upper Schieferhulle. Innsbruck AA LSH BP FH-1M ZG AA USH 10 km ZG EZ N Photo to right: J. Selverstone sampling in the Tauern Window. The sample studied in detail for garnet zoning is from a rock unit called garben schist because of the large hornblende crystals that roughly resemble bundles of wheat ( garben in German) (see photo at left). Many samples contain spectacularly large garnets

22 F. S. Spear Program Gibbs Tutorial 54 Garben schists contain a range of assemblages that include subsets of the phases hornblende, kyanite, staurolite, garnet, biotite, epidote, plagioclase, ankerite, quartz, ilmenite, and rutile with either paragonite or chlorite. The sample studied in detail contained the sub-assemblage hornblende + kyanite + staurolite + garnet + biotite + epidote + plagioclase + quartz + chlorite which, with fluid, is divariant in the system CNKFMnMASH. Photomicrograph of sample FH-1M. Field of view is approximately 1 cm. Xsps Xalm Garnet in sample FH-1M is strongly zoned with bell-shaped spessartine and grossular, increasing pyrope, and almandine that shows a maximum. Fe/(Fe+Mg) FH-1M X grs Fe/(Fe+Mg) X alm X sps 7 7 X prp Fe/(Fe+Mg) Xgrs Xprp decreases monotonically from core to rim suggesting T increased throughout garnet growth Ṫhe input data for the rim P-T conditions are contained in the files named IN-TAUERN WIND rim. We will use these data to reproduce the calculations published by Selverstone et al. (1984). rim core rim Distance mm

23 F. S. Spear Program Gibbs Tutorial 55 1) From the MAIN menu, select option 1 (BEGIN/SAVE) and open the disk file named IN-TAUERN WIND rim. The assemblage present in the matrix of the rock is garnet + biotite + chlorite + kyanite + staurolite + hornblende + plagioclase + quartz. Evidence was given by Selverstone et al. (1984) that this assemblage was present during entire growth of garnet. 2) Go to SINGLE STEPS menu (option 2 from the MAIN MENU). Note that the variance of the assemblage is 2 and we have 3 independent compositional parameters from the zoning in the garnet (X Almandine, X Spessartine, X Grossular ). Also, we know the composition of the plagioclase in the matrix of the rock (An 32 ) and in the core of the garnet (An 18 ). There are several ways we could tackle this problem. (A) We could select 2 of the 4 possible monitor parameters and check to see how the other two calculate (compare the computed core composition with the actual core composition). We could then pick a different pair of monitors and see how the results compare with the first set. This is the procedure we will follow first using first almandine and grossular as monitors and then using spessartine and plagioclase. Note that it would not be a good idea to choose almandine + spessartine or grossular + anorthite as monitors because almandine and spessartine are both T sensitive and P insensitive and grossular and anorthite are both P sensitive but relatively T insensitive. This could generate large errors in T or P from low-angle intersections. (B) Alternatively, we could try and find a "sensible" way to increase the variance (wouldn't it be nice if rocks were always be this well constrained). One possibility is to allow Pfluid to be an independent variable. In this way we could guarantee that 3 of the 4 monitors fit perfectly, and use the fourth as a check. We'll try this too. Below is a table containing the garnet and estimated plagioclase composition from the garnet rim to the core, expressed as changes in composition for 6 increments. Increment XAlm XGrs XSps XAnor (estimate) (core) ) Select SINGLE STEPS option 2 (CHOOSE MONITORS). Choose XAlm and XGrs as monitors and set XAlm = and XGrs = Choose NSTEP = 10. 4) Select SINGLE STEPS menu option 4 (COMPUTE 1 INCREMENT). The P-T path for the first increment should be drawn on screen. 5) Repeat (7) and (8) using zoning increments 2-6 to draw the entire P-T path. Your plot should look like this (red curve):

24 F. S. Spear Program Gibbs Tutorial Sample FH-1M Tauern Window P kbar core Alm+Grs monitors 6 4 Sps+Plg monitors rim T (C) The P-T path can be compared with that published by Selverstone et al. (1984) (note different scales). You will notice that the published P-T path has a shape very similar to the one we just calculated, but the absolute values of T and P are different. The published path shows T -20 C, P +3.5 kbar (at maximum pressure) whereas the one we computed shows T -75 C, P +3.5 kbar. The discrepancy in the calculated T most likely results from the different thermodynamic data set used. In particular, Selverstone et al. (1984) used a constant value for the entropy of water whereas the current program uses a value that is a function of P and T. It is useful to compare the compositions that are computed for the core of the garnet with the measured compositions. Because the variance of the sample is 2, we have this check on the calculations. 6) Select SINGLE STEPS option 7 (PRINT DATA TO SCREEN AND FILE). The current status of the assemblage will appear: ************************************************************************ T P Pfluid START CURRENT MONITOR PARAMETERS-- NSTEP= 10 IMASS= 0 4 X_Alm 6 X_Grs System components Si.. Al.. Mg.. Fe.. Mn.. Ca.. Na.. K... H2O. Mass balance = OFF # OF PHASES, NPH= 9 Mineral compositions

25 F. S. Spear Program Gibbs Tutorial 57 PhCo X(i) dx(i) sumdx(i) 1 Quartz-(a-b) abqz Water H2O Kyanite Ky Plagioclase-ideal_solution Ab An Garnet-ideal_1-site_mixing Prp Alm Sps Grs Biotite-(FE-Mg-Mn)_ideal_1_site_ Phl Ann MnBt Staurolite-ideal MgSt FeSt MnSt Chlorite-( )-ideal_1-si Chlin Daph MnChl Hornblende(Mg-Fe-Mn)-ideal_1-sit Mg-Hb Fe-Hb Mn-Hb The calculated concentrations for the core of the garnet for spessartine, anorthite and Fe/(Fe+Mg) in the amphibole are , 0.121, and 0.47, respectively, compared with the measured values of 0.122, 0.18, and This agreement is fair, and all of these changes are in the correct direction. It is of course possible to "force" any two calculated "core" compositional variables to match the measured values by choosing those variables as monitor parameters. For example, X Anorthite and X Spessartine could be forced to fit perfectly if these values were chosen as monitors. This exercise is worth doing because it gives a feel for the sensitivity of the P-T path to choice of monitor parameters. 7) Reset the mineral assemblage to the starting conditions (SINGLE STEPS option 6, then type 3). 8) Recalculate the P-T path, this time using X Sps and X Anor as monitor parameters. Select a square for the symbol. Choose option 2 to set the appropriate monitor parameters and deltas, then calculate the path using option 4. Repeat options 2 and 4 with the appropriate values of X Sps and X Anor. The final P-T path is shown above in green. ************************************************************************ T P Pfluid START

26 F. S. Spear Program Gibbs Tutorial 58 CURRENT MONITOR PARAMETERS-- NSTEP= 10 IMASS= 0 5 X_Sps 3 X_An System components Si.. Al.. Mg.. Fe.. Mn.. Ca.. Na.. K... H2O. Mass balance = OFF # OF PHASES, NPH= 9 Mineral compositions PhCo X(i) dx(i) sumdx(i) 1 Quartz-(a-b) abqz Water H2O Kyanite Ky Plagioclase-ideal_solution Ab An Garnet-ideal_1-site_mixing Prp Alm Sps Grs Biotite-(FE-Mg-Mn)_ideal_1_site_ Phl Ann MnBt Staurolite-ideal MgSt FeSt MnSt Chlorite-( )-ideal_1-si Chlin Daph MnChl Hornblende(Mg-Fe-Mn)-ideal_1-sit Mg-Hb Fe-Hb Mn-Hb Note that the final P-T conditions differ somewhat from those computed earlier. Also note that now the spessartine and anorthite compositions match the measured core compositions, but the computed X Alm = compared with the measured value of 0.633, the computed and measured grossular core values are and 0.167, respectively, and the computed and measured hornblende core values are 0.44 and 0.518, respectively. This match is not perfect, as it should be if the rock were being modeled perfectly and hints that there may have been other factors involved in the metamorphism of this sample.

27 F. S. Spear Program Gibbs Tutorial 59 Appendix: Making a Gibbs input file This first exercise will demonstrate the making of making an input file for the Gibbs program. The file we will make will be for the assemblage muscovite + biotite + Al2SiO5 + quartz + K-feldspar + H2O in the KFASH system. This assemblage is univariant and we will use the input file in exercise 2 to draw a univariant curve (the muscovite breakdown reaction). 1) Start program Gibbs 2) Select the Gibbs Tutorial thermodynamic data file 3) Choose menu item 1 (Begin/save a problem) 4) Choose submenu item 3 (Create a new input file) a) In the dialog box, give the assemblage a title (e.g. Ms+Bt+AlSi+Qtz+Kfs+H2O - KFASH), Click the appropriate boxes for the KFASH system and specify the starting T and P to be 770. C, 8733 bars. The dialog box should look like this: b) Select from the mineral list i) For quartz, H2O, AlSi and K-feldspar, there are no composition data to enter, so when the mineral dialog box appears, just click "done" ii) a-b quartz (mineral number 1). This mineral will switch between alpha and beta quartz according to their relative stability fields. iii) H2O (mineral number 2)

28 F. S. Spear Program Gibbs Tutorial 60 iv) Al-Silicate (mineral number 8). This mineral will switch between kyanite, sillimanite and andalusite, depending on the P-T conditions. v) K-feldspar (mineral 92). This mineral contains disorder terms, so it will change structural state with temperature. vi) Muscovite (mineral number 117). Muscovite 117 is a muscovite-celadonite solid solution. Input values of XFecelad and Xms of 0.1 and 0.9, respectively: vii) Biotite (mineral 119). Input values of Si = 2.5, Al(iv) = 1.5, Al(vi) =.5, Mg = 0, Fe = 2.5. viii) Click cancel on the mineral selection list. 5) Click on the "New Input File" window and save using "Saveas" command from the file menu. Name the file "KFASH MsBtAlSiKfsQtzH2O". 6) Click on the "Command" window and hit return to close "New Input File" window. Now you can open the data file for use in Gibbs.