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The stability of MG-chlorite McPhail, Derry Campbell 1985

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THE STABILITY OF M(> CHLORITE by DERRY CAMPBELL MCPHAIL B.Sc, The University of British Columbia, 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Geological Sciences We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1985 © Deny Campbell McPhail, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of n r J O L O G , tCJVL. ?C-ir~ fQC(=-£ The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 n/R'n Abstract The equilibrium Chlorite = Cordierite + Forsterite + Spinel + H 2 0 has been experimentally determined with a chlorite of composition Mg^sAl^Si^sO^OH),. Brackets have been obtained between 605 and 640° C at 0.5 kb, 644 and 670° C at 1.0 kb and 690 and 704° C at 2.0 kb. These data are not notably displaced from Chernosky's (1974) data for the same equilibrium with a chlorite of clinochlore composition (IvJ^A^SijOioCOH^), however they are more constraining. A thermodynamic analysis of the above data and data on related equilibria included ideal solution models describing compositional variability in cordierite, orthopyroxene and chlorite. The H 2 0 content of cordierite was described using a model based on that of Newton and Wood (1979). The hydrous end-member has two moles of H 2 0 and the volumes of the end-members are different; this allows the full range of data to be described with one function. Al-content of orthopyroxene was calculated with Gasparik and Newton's (1984) model. Solid solution in chlorite was modelled by choosing the end-members, Mg 6Si 4 O 1 0 ( O H ) s and Mg 4Al 4Si 2 O i 0 ( O H ) 8 , and using ideal configurational entropy to describe the free energy of mixing. Disordering phenomena in cordierite and spinel were accounted for by adding small entropies of disorder to the third law entropies. Linear programming was used to calculate consistent thermochemical properties for all phases considered. Experimental results indicate that the upper thermal stability of Mg-chlorite is affected by only a few degrees for the composition used here. The thermochemical properties derived allow more complete modelling of systems that include chlorite. ii TABLE OF CONTENTS Abstract ii Table of Contents iii List of Tables iv List of Figures v Acknowledgements vi INTRODUCTION : 1 EXPERIMENTAL M E T H O D 4 Starting Materials 4 Technique 4 Phase Characterization 5 Results 10 a T H E R M O D Y N A M I C ANALYSIS 12 Cordierite 12 Crystal chemistry. , 12 Thermodynamic model 15 Experimental data 16 Fitting procedure 20 Results 23 Orthopyroxene 24 Spinel 26 Chlorite 27 Linear Programming Analysis 28 Phase equilibrium data 28 Constraints 32 Fitting procedure 33 Results 35 CONCLUSIONS 39 REFERENCES 40 iii LIST OF TABLES Table I. Symbols, abbreviations and compositions 3 Table II. D-spacings and refined cell parameters for synthetic chlorites Mg 4 . , 5 AJ^ 5 Si 2 . 7 5 0 1„(OH) 8 and Mg 5 Al 2 Si 3 O 1 0 (OH) 8 8 Table III. Experimental data on the equilibrium: Chlorite = Cordierite + Forsterite + Spinel + H 2 0 11 Table IV. Heat capacity coefficients for phases and species considered in this study: Cp = k„ + k / T " + k 2 / P + k , / T (J/mol-K) 13 Table V. Cordierite hydration data used in the calibration of the cordierite hydration model 19 Table VI. Changes in enthalpy, entropy and volume for anhydrous and hydrous cordierite end-members 24 Table VII. Phase equilibria data for equilibria (1) through (5) 29 Table VIII. Volumes of Mg-chlorites 33 Table IX. Calculated enthalpies of formation from the elements, third law entropies and molar volumes for phases and species used in this study 36 iv LIST OF FIGURES Figure 1. Representative x-ray powder diffraction pattern for the synthetic chlorite used in this study 7 Figure 2. Mg-chlorite volumes as a function of Al-content 9 Figure 3. Diagrammatic representation of the generation of brackets from the cordierite hydration data 21 Figure 4. Isopleths of cordierite, n H Q represents the number of moles H20 per unit formula 22 Figure 5. Water content of Mg-cordierite in equilibrium with H20 as a function of pressure and temperature 25 Figure 6. The equilibrium Chlorite = Cordierite + Forsterite + Spinel + H20 37 Figure 7. The upper thermal stability of Mg-chlorite 38 v ACKNOWLEDGEMENTS There are many people who deserve acknowledgement for their parts in this study. Dr. H.J . Greenwood has provided academic, financial and moral support throughout most of my academic career, and Drs. Brown and Meagher and Ross have also contributed to my academic upbringing. The technical staff have indulged many of my follies, especially E d Montgomery and Lyle Hammerstrom. M y fellow graduate students, notably Paul Bartholomew, have provided many a stimulating discussion, although not always in my specific area, and for this I am grateful. The person responsible for much of the inspiration for this work, and a lot of the groundwork necessary is Rob Berman. I would like to express my deepest gratitude for all that he has done. There is one more group of people that deserve deep appreciation, my wife, Maria; my daughter, Christina; my son, Sean; my mother; and a special note for my dad - I wish he had lived to see me finish. I thank all of the people above, and more, for all the help and encouragement you have given me. vi 1 INTRODUCTION The upper thermal stability of chlorite in the system M g O - A l 2 0 3 - S i 0 2 - H 2 0 has been experimentally investigated in a number of studies. The equilibria limiting this stability are, with increasing pressure, 5 Chlorite = 1 Cordierite + 10 Forsterite + 3 Spinel + 20 H 2 0 (1) (Fawcett and Yoder, 1966; Chernosky, 1974; this study), 1 Chlorite = 1 Orthopyroxene + 1 Forsterite + 1 Spinel + 4 H 2 0 (2) (Fawcett and Yoder, 1966; Staudigel and Schreyer, 1977; Jenkins, 1981) and 2 Chlorite = 1 Pyrope + 3 Forsterite + 1 Spinel + 8 H 2 0 (3) (Staudigel and Schreyer, 1977). Invariant points are generated by the intersections of equilibria (1) and (2) and by (2) and (3). Of the equilibria generated from these invariant points two have been experimentally determined, 1 Cordierite + 5 Forsterite = 5 Orthopyroxene + 2 Spinel (4) (Fawcett and Yoder, 1966; Seifert, 1974; Herzberg, 1983) and 2 Orthopyroxene + 1 Spinel = 1 Pyrope + 1 Forsterite (5) (Danckwerth and Newton, 1978; Perkins et al., 1981; Gasparik and Newton, 1984). The stoichiometric coefficients in the above equilibria are for chlorite of clinochlore composition, orthopyroxene of enstatite composition (6 oxygen formula unit) and anhydrous cordierite. Both solid solution and/or site and stacking disorder affect some of the phases involved. Chlorite has a variable aluminum content (Fawcett and Yoder, 1966) and stacking disorder (Spinnler et al., 1984). There is also the possibility of disorder on the tetrahedral and octahedral sites. Cordierite has a variable volatile content that is a function of pressure, temperature and coexisting fluid phase (Schreyer and Yoder, 1964; Johannes and Schreyer, 1981) and possible disordering on the tetrahedral sites (Gibbs, 1966). There is also the possibility of disordering the volatile channel-site species. The aluminum content of orthopyroxene varies as a function of pressure, temperature and stable assemblage (Wood, 1974) and ordering of octahedral aluminum in Mg-orthopyroxenes has been described (Ganguly and Ghose, 1979). Solid solution in spinel between M g A l 2 0 4 and A1 20 3 has been documented (Roy et al., 1953; Navrotsky and 2 Kleppa, 1967) and spinel can exhibit significant disorder between the normal and inverse structures (Navrotsky and KJeppa, 1967). Non-stoichiometric behaviour in forsterite and pyrope has not been documented, at least for the range of conditions considered here, and for the purposes of this study H 2 0 is considered to be pure. Many of the above problems have been addressed experimentally and theoretically, however the effect of variable aluminum content in chlorite has not been determined. One of the purposes of this study was to experimentally determine this effect on equilibrium (1), the low pressure, high temperature breakdown of chlorite. The other purpose was to combine the new data with existing data on equilibria (1) through (5) and activity models for non-stoichiometric behaviour to calculate internally consistent thermochemical properties for the phases involved. The derived properties will allow more precise calculation of the upper thermal stability of chlorite as well as other equilibria involving chlorite. 3 Table I Symbols, abbreviations and compositions AGr(P,T) AG°(P,T) AG H 2 0(P,T) A f H°(Pr ,Tr) AH r(P r ,Tr) AH s(P r ,Tr) S° AS»(Pr ,Tr) V ACp r ACp, x ; X s chl coph cord herd xOpx xEn Chlorite (Chl) Clinochlore (Clin) Chls (Chls) Corundophyllite (Coph) Cordierite (Cord,Cd) Enstatite (En) Forsterite (Fo) Orthopyroxene (Opx) Pyrope (Py) Spinel (Sp) Free energy change for a reaction at pressure and temperature. Free energy change of a reaction for the phases in their standard state at pressure and temperature. Free energy of formation from the elements of H 20 at pressure and temperature. Enthalpy of formation from the elements of a phase at 1 bar and 298.15 K. Enthalpy of reaction at 1 bar and 298.15 K. Enthalpy of reaction for the solid phases in a reaction at 1 bar and 298.15 K. Third law entropy for a phase. Third law entropy change of reaction for the solid phases. Molar volume of a phase. Volume change of reaction for the solid phases in a reaction. Heat capacity change of reaction. Heat capacity change of reaction for the solid phases in a reaction. Mole fraction of corundophyllite (Mg 4Al 4Si 2 Oi 0(OH) 8) in chlorite. Mole fraction of hydrous cordierite ( Mg 2Al 4Si50n -2H 20 ) in cordierite. Mole fraction of enstatite (Mg 2Si 20 6) in orthopyroxene. Mg 6Si 4O 1 0(OH) E-Mg 4Al 4Si 2O 1 0(OH) g Mg 5Al 2 Si3O 1 0(OH) s Mg 6Si 4O 1 0(OH)3 Mg 4Al 4Si 2O 1 0(OH) 8 Mg 2Al 4Si 50 1 8-nH 20 Mg 2Si 20 6' Mg :Si0 4 Mg 2Si 20 6-MgAl 2Si0 6 Mg,Al 2Si 30 1 2 MgA.1,0, 4 E X P E R I M E N T A L M E T H O D Starting Materials An oxide mix was prepared from reagent grade chemicals in the molar proportions 4.75MgO : 1.25A1203 : 2.75Si02. Periclase (MgO) was prepared by baking MgO (Fisher Certified Reagent-Lot #741694) for approximately 24 hours at 1300° C and cristobalite (Si0 2) by baking silicic acid (Fisher Certified Reagent - Lot #730944) for approximately 24 hours at 1300° C. K-A1 20 3 was prepared from Al(0H)3-nH20 (Fisher Certified Reagent - Lot #745229) by baking at 400° C for four hours, 700°C for one hour and 1000° C for one hour. The oxides were ground under alcohol and dried in a vacuum furnace for approximately 24 hours at 120° C before use. Appropriate proportions were carefully weighed out and the mix was ground for approximately two hours under distilled water in an agate mortar. To ensure homogeneity the mix was periodically dried and collected into the bottom of the mortar. The resulting mix was then dried and stored in a dessicator. Chlorite was synthesized from the oxide mix plus approximately 25 wt% distilled water in two steps - 4kb, 400° C, 7 to 10 days and 4kb, 700° C, 14 to 18 days. The first step helped prevent extraneous phases such as spinel and forsterite from nucleating and the second annealed the structure to the 14AIIb (Bailey and Brown, 1962) polytype. A trace of spinel was identified optically but not in amounts large enough to significantly affect the composition of the chlorite. The amount of spinel was estimated to be less than 0.1 volume percent from the Comparison Charts for Visual Estimation of Percentage Composition (Terry and Chilingar, 1955). If spinel is the only extraneous aluminous phase and the volumes of spinel and chlorite are taken to be 40 cm3 and 210 cm3 respectively then the change in the chlorite composition is calculated to be less than 0.01 atoms of aluminum per formula unit The high temperature assemblage (cordierite, forsterite and spinel) was synthesized from slightly impure chlorite obtained in earlier, less successful, chlorite syntheses. The synthesis conditions were 2 kb, 740° C and 14 days. No impurities were detected by either x-ray diffraction or optical methods. Technique All experiments were conducted in standard cold seal pressure vessels of either Stellite K.-25 or Rene 41 alloys. The furnaces are horizontally mounted and wound with coiled nichrome wire. Temperatures were measured with sheathed chromel-alumel thermocouples mounted in an external well designed to hold the thermocouple tip close to the sample. The configuration was calibrated at one atmosphere between 300° C and 800° C and the temperature gradients were found to be less than ±1°C over the three centimetre length of the sample capsule. Temperature was controlled by fully 5 proportional controllers that normally control to less than ± 1° C. Precise daily measurements were made using either a temperature compensated digital thermometer with a resolution of 1°C or a potentiometer with an estimated resolution of 0.1° C. Temperature was not monitored continuously so an effort was made to make measurements at different times of day to avoid any possible systematic differences. No systematic differences were noted. Quoted temperatures are the means of the daily measurements (corrected by the calibration determinations) and the associated errors are sums of two standard deviations, gradient uncertainties and an estimated 3° C for thermocouple calibration uncertainties. The pressure media were either methane or distilled H 20. Measurements were made every one to three days, usually daily, with either an Ashcroft Maxisafe gauge with a resolution 15 bars or a Heise Bourdon tube gauge with a resolution of 5 bars. Experiments with pressure drops of more than 3% were not considered successful. The quoted pressures are the means of the measurements and the associated errors are sums of two standard deviations plus an estimated 20 bars for gauge accuracy. The starting materials for reversal experiments were made of two mixtures of reactants and products: 15-20 wt% of the reactants plus 80-85 wt% of the products; and 80-85 wt% of the reactants plus 15-20 wt% of the products. Each run consisted of two experiments in a single pressure vessel, one capsule with the first mixture and the other with the second mixture. Gold capsules were loaded with 10 to 20 mg of mix plus approximately 25 wt% distilled H 20, then sealed, weighed and loaded into the pressure vessel. Runs were brought to temperature in about one half hour and stabilized within two hours. Quenching was accomplished by placing the vessel into a cooling jacket and blowing compressed air around the vessel. The temperature dropped more than 250° C within the first minute and to less than 100° C after five minutes. The remaining pressure was released and the capsules were removed, weighed, punctured, dried, reweighed and then opened for examination. Only runs that showed no weight loss during the experiment were used. Results were examined optically and by x-ray diffraction and if complete reaction had not occurred the reaction direction was determined by examining x-ray diffractograms and analyzing peak height ratios. Estimated changes in peak heights of at least 30% for chlorite and lesser but opposite amounts for cordierite, forsterite and spinel were taken as unequivocal indication of reaction. Experiments that resulted in lesser changes were considered indeterminate. Phase Characterization All solid phases were identified by optical properties, x-ray diffractograms and morphology. Chlorite was characterized by a bulk refractive index and by a cell refinement from powder diffractograms. Precise characterizations of cordierite, forsterite and spinel were not considered necessary as their x-ray patterns and optical properties agreed with published data. Also, the non-stoichiometric behaviour of 6 cordierite has been well studied elsewhere and the disorder in spinel was not determined in this study. Chlorite occurred as fine grained aggregates of crystals ranging in size from less than one micron to two microns. The small grain size and the aggregate habit precluded an accurate measurement of the refractive indices and therefore only a bulk index was measured. The refractive index was bracketed between 1.572 and 1.580 in white light This compares well with indices of 1.581 to 1.586 quoted for clinochlore and approximately 1.576 for a chlorite of the composition studied here (Troger, 1979. pages 116-118). A representative x-ray powder diffraction pattern is shown in Figure 1 to demonstrate the crystallinity of the chlorite starting material. The structure is the lib polytype (notation of Bailey and Brown, 1962). In order to refine the cell parameters of the chlorite used here, four scans (two with increasing 20 and two with decreasing 20) were made using silicon metal (a = 5.4305A) as an internal standard, CuKa radiation and a scan rate of 1/4° 20/minute. The means of the peak positions were calculated and the corresponding d-spacings were used in the program of Evans et al. (1963) to calculate refined cell parameters. Observed and calculated d-spacings and the refined cell parameters are presented in Table II. Also shown are data from Chernosky (1974) for synthetic clinochlore. The a, b and c cell parameters all somewhat smaller than those determined by Chernosky and /3 is the same within one standard deviation. The d-spacing of (001) as a function of aluminum content has been calibrated in a number of studies: Brindley and Gillery (1956) - naturals, Nelson and Roy (1958) - synthetics, Gillery (1959) - synthetics, Albee (1962) - naturals, Shirozu (1972) - synthetics. The curves determined in these studies are shown in Figure 2. Natural chlorites appear to show a greater dependence of d(001) on Al-content but the chlorites used in those calibrations contain impurities, mainly iron. It is not clear if the impurities have an effect on the basal repeats. Also shown in Figure 2 is the value of d(001) for the chlorite synthesized in this study. The calculated value of d(001) agrees well with the curves derived from synthetics and is slightly larger than those of the naturals. No evidence was found to indicate the presence of a 7 A phase noted by Chernosky (1974). He quotes the intensities for the basal repeats (001), (002), (003) and (004) to be all of equal intensity (based on estimates from a Debye- Scherrer film pattern). The intensities of the basal repeats for the chlorite in this study have ratios of (001)/(002) and (003)/(004) equalling 0.42 and 0.84 respectively and these ratios appear to remain constant over the length of the experiments. This might represent some sort of stacking disorder but without independent evidence or more study no conclusions can be made. Cordierite was identified as hexagonal prisms as large as 100 microns in length. Miyashiro (1957) proposed the A index to measure the degree of Al/Si disorder in'cordierite. More recent evidence shows this index to be also a function of composition (Selkregg and Bloss, 1980) and long range versus short range order (Putnis, 1980). As a result the A index has not been used in this study. Figure 1. Representative x-ray powder diffraction pattern for a synthetic chlorite with composition Mg,. ? 1 A] l ! S i i , i O, ( , (OH) 8 . The scan was made at 2' 2 0/min with nickel filtered copper radiation and the scale is approximately 40(1 counts per second. The first five orders of the basal repeat are not shown completely in order to show other peaks more clearly. Table II D-spacings and refined cell parameters for synthetic chlorites, Mg4.75Al2.5Si2.75O , . ( O H ) , and M g 5 A l 2 S i 3 O 1 0 ( O H ) 8 Synthetic Clinochlore chlorite Chernosky (1974) Mg4.75Al2.5 Si 2 . 7 J Oio(OH), Mg 5Al 2Si 30 1 ( ) (OH) 1 h k 1 d(calc)1 d(obs) I(/100)2 d(obs) 0 0 1 14.234 XX 14.132 0 0 2 7.117 XX 7.135 0 0 3 4.745 4.752 XX 4.757 0 2 0 4.596 4.592 40 1 1 0 5.576 — 4.588 1 1 1 4.500 4.501 30 4.493 0 2 1 4.374 4.384 25 4.373 1 1 1 — 4.242 1 1 1(?) 4.226 4.238 20 1 1 2 4.053 4.055 20 0 2 2 3.861 3.862 15 3.883 1 1 2 3.674 20 3.674 0 0 4 3.558 3.560 XX 3.572 0 0 5 2.847 2.846 XX 2.864 1 1 4 2.673 — 2.691 2 0 1 2.654 2.653 15 2.656 2 0 2 2.580 2.579 35 • 2.584 2 0 1 2.539 2.538 100 2.540 2 0 3 2.438 2.437 80 2.441 0 0 6 2.380 2.376 40 2.385 2 0 4 2.257 2.258 35 2.260 2 0 5 2.258 2.258 20 0 0 7 2.033 2.034 35 2.041 2 0 4 2.004 2.004 85 2.008 2 0 6 1.884 1.885 35 1.889 2 0 5 1.826 1.826 35 1.831 0 0 8 1.779 1.781 10 2 0 7 1.717 — 1.724 2 0 6 1.665 15 1.671 2 0 8 1.568 1.568 55 1.573 0 6 0 1.532 1.532 70 1.539 0 6 2(?) 1.498 1.501 20 1.502 0 6 3 1.458 — 1.463 1 1 9 1.448 — 1.455 0 010 1.424 1.423 20 3 3 3 1.409 ' — 1.412 2 0 8 1.397 1.397 50 1.402 4> 5.317(1) 5.324(1) 9.192(2) 9.224(3) c(A) 14.349(2) 14.420(5) 97°8'(1') 97°6'(1') V(cm3/mole) 209.515(51) 211.535(84) 'All d-spacings are given in A. intensities are given relative to (201) (see Figure 1). The intensities of the peaks for the first five orders of the basal repeat are discussed in text ? Assumed Miller indices. 9 14.60 o < O O 14.40 - - - ^ b 14.20 -14.00 13.80 C h l C o p h Figure 2. Mg-chlorite volumes as a function of Al-content. A. Brindley and Gillery (1956) - calibrated from natural Fe-Mg chlorites (data range from 0.4-0.8x^h). ..chl B. Nelson and Roy (1958) - synthetic Mg-chlorites (data range from 0.5— l - U x coph^" C. Gillery (1959) - synthetic Mg-chlorites (data range from 0.25-1.0x^ph). D. Albee (1962) - natural Fe-Mg chlorites (data range from 0.3-0.8x^h). .chl E. Shirozu and Momoi (1972) - synthetic Mg-chlorites (data range from O-3-l-Ox^ ^ J. F. This study - synthetic Mg-chlorite, box represents approximately two standard deviations ..chl in d-spacing. The error in composition was a maximum of ± .Olx coph" 10 Spinel usually occurred as euhedral grains of less than 1 micron in size although a few octahedral grains up to 2 microns were noted. Forsterite was identified as anhedral to euhedral grains of platy habit with a range in size from 1 to 20 microns. No evidence of non-stoichiometric behaviour was observed in either forsterite or spinel. This is consistent with the findings of Chernosky (1974) in his study of clinochlore stability. Results Experimental reversals of equilibrium (1) (Chl=Cd+Fo+Sp+H 20) were made at pressures of 0.5,1.0 and 2.0 kilobars. The conditions and results of the experiments are listed in Table III. Fawcett and Yoder (1966) note shifts in the chlorite composition and therefore care was taken to monitor any such shifts. This was done by measuring (004) and higher order basal peaks against forsterite and spinel peaks before and after the experiments. Within the precision of measurement no shift in the peaks was noted. The precision corresponds to approximately 0.1 atoms of aluminum per formula unit Chernosky (1974), in his study of the same equilibrium using clinochlore, also finds no shift in peak positions. The composition of chlorite is therefore considered to remain constant during the course of the experiments. Non-stoichiometric behaviours in cordierite and spinel were not measured for the following reasons. The variable water content of cordierite was not measured as the quench rates were not sufficient to prevent rehydration. In addition, pressures and temperatures were outside the 'quenchable' region shown by Medenbach et al. (1980). The degree of order in spinel could not be measured because of small grain size. There are powder diffraction techniques available to measure order in spinels (eg. Furuhashi et al., 1973) but they are not suitable for the Mg-Al spinel considered here. These techniques measure the difference between the theoretical and observed intensities of the diffraction patterns. The theoretical intensities are calculated based on the scattering factors of the elements involved. Magnesium and aluminum have similar scattering factors and therefore the calculated intensities are not very sensitive to ordering in the structure. 11 Table III Experimental data on the equilibrium: Chlorite Chlorite composition: Mg4.75Al2.jSi2.75Oio(OH)8 = Cordierite + Forsterite + Spinel + H20. Run # Chi-124b 1 Chl-130a,b 1 Chl-131a,b Chl-120a,b C h i - 128a Chi-125b Chi-129a Chl-112a.b Chi-101 P(bars) 500(20)' 500(25) 500(25) 500(25) 500(20) 1000(25) 1000(30) 1000(20) Chl-121a,b 1000(20) Chl-113a,b 1000(50) 2000(50) Chl-132a,b 2000(30) Chl-114a,b 2000(50) Chl-133a,b 2000(50) Chl-115a,b 2000(50) T(°C) 594(7) 605(5) 629(5) 633(6) 640(5) 644(5) 670(4) 673(5) 679(7) 692(5) 690(10) 704(5) 705(5) 719(5) 729(5) Duration Results 487(hrs) 884 884 480 516 487 520 480 482 480 480 759 480 742 480 b-80% reaction to C h l 3 (chl peaks diffuse) a-80% to Chi b-80% to Chi a-no apparent reaction b-no apparent reaction a-no apparent reaction b-no apparent reaction 10% to Cd + Fo+Sp 80% to Chi (chl peaks diffuse) 30% to Cd + Fo+Sp a-10% to Cd + Fo + Sp b-100% to Cd + Fo + Sp a- no reaction 4 b-100% to Cd + Fo+Sp a-100% to Cd + Fo+Sp b-100% to Cd + Fo+Sp appearance of Chl (St. mat -Cd + Fo+Sp) a-20% to Cd + Fo+Sp b-100% to Cd + Fo+Sp a- no reaction 4 b-100% to Cd + Fo+Sp a-100% to Cd + Fo+Sp b-100% to Cd + Fo+Sp a-100% to Cd + Fo + Sp b-100% to Cd + Fo+Sp 1 a represents 4:1 mixture of reactants and products, b represents 4:1 mixture of products and reactants. 3 Numbers in brackets represent errors in the last significant digit(s) of the quoted values. 3 x % represents the estimated percentage change in ratios of reactants to products. 4 The starting material is pure chlorite. 12 T H E R M O D Y N A M I C A N A L Y S I S A thermodynamic analysis of the experimental data was used to test for internal consistency, both within the data itself, and with other related experimental data. Thermochemical properties (heat capacities, enthalpies, entropies and volumes) for all the phases considered in this study were either adopted from existing sources or derived to be consistent with existing phase equilibria and calorimetric data. The heat capacity function and the coefficients used in this study are from Berman and Brown (1985): Cp = k 0 + k/T 0- 5 + k 2/T 2 + k,/T. (6) Table IV lists the coefficients for the phases considered here. Compressibilities and expansivities were not considered in this study. The enthalpies, entropies and volumes of the phases involved were constrained, where data exists, to be consistent with that data. If constraining data did not exist then estimates were made. The free energy of H 2 0 was calculated using a combination of the routines of Haar et al. (1979) and Delany and Helgeson (1978). Below 10 kilobars the Haar et al. routine was used and above 10 kilobars the Delany and Helgeson routine was used (see Berman, 1985). The reference states of enthalpy and entropy for H 2 0 were those of water from C O D ATA (1978). Forsterite and pyrope were treated as stoichiometric phases and therefore the calculation of their free energy is straightforward. The other phases (cordierite, orthopyroxene, spinel and chlorite) are affected by non-stoichiometric behaviour and the calculation of the resulting free energy contributions for each is outlined below. Cordierite The thermodynamic characterization of cordierite is complicated by its variable composition and by possible disordering on the tetrahedral sites. Cordierite contains varying amounts of H 2 0 (in the chemical system studied here) which is a function of pressure and temperature. Several comprehensive models have been presented to describe this behaviour (Newton and Wood, 1979; Lonker, 1981; Martignole and Sisi, 1981) but none of them reproduces the existing hydration data adequately. A new model is presented here to provide a single function to describe the H 2 0 content over the full range of existing P-T data. Crystal chemistry The crystal chemistry of cordierite has been well studied and is discussed in detail by Wallace and Wenk (1980), Hochella et al. (1979), Cohen et al. (1977), Meagher and Gibbs (1977) and Gibbs (1966). 13 Table IV Heat capacity coefficients for phases and species considered in this study: Cp =. k0 + k,/^5 + k 2/P + k 3/P (J/mol-K). Phase (species) Clinochlore M g JAl JSi , 0 1,(OH), Chls Mg 6Si«0„(OH), Coph Mg 4Al 4Si 2O 1 0(OH) 8 Cordierite Mg 2Al 4Si 50 1 8-nH 20 Enstatite Mg 2Si 20 6 Forsterite Mg 3Si0 4 Pyrope Mg 3Al 2Si 30 1 2 Spinel MgAl 20 4 ki 1213.28439 1200.38715 1228.18163 937.62415 333.15900 238.64137 640.72000 235.89993 •306475. 306475. •11023143. -4541120. 0. •4701900. -1710415. -11217.1299 -10925.2168 -11509.0430 -7166.2532 -2401.1760 -2001.2607 -4542.0690 -1766.5781 k3 -1256253287. -1167926773. -1344579801. 1425736441. 558300800. -116243280. 0. 40616926. Briefly, cordierite (MgjALSisOis-nHiO) is a framework silicate made of six-membered rings of silicon and aluminum tetrahedra stacked along the c-axis. The rings are connected by three alumina and silica tetrahedra and form channels that allow constituents to pass through the structure. In the channels and between the rings are cavities where ions and molecules may reside. H 20 molecules were the only species considered in this study. Two naturally occurring 'polymorphs' have been recognized, cordierite (orthorhombic) and indialite (hexagonal). They have been thought to be related through a process of continuous tetrahedral aluminum disordering with indialite being completely disordered (Miyashiro, 1957). However, Meagher and Gibbs (1977), in a single crystal refinement of indialite from the type locality, find a significant degree of order in the structure. They estimated the Bragg-Williams long range order parameter, z, to be 0.38 (z = 0 for full disorder). Putnis and Bish (1983) synthesized cordierites with a range of structural states by annealing stoichiometric Mg-cordierite glass in air. The conditions of synthesis were temperatures of between 14 1000° C and 1400° C for periods of 15 minutes and 3 hours respectively. The resulting synthetic cordierites were studied by high resolution transmission electron microscopy and showed local ordering. They found by using longer synthesis times orthorhombic cordierite resulted. Schreyer and Schairer (1961a) estimated the transition temperature between the two 'polymorphs' to be greater than 1440° C at one atmosphere. These lines of evidence indicate that at temperatures below at least 1400° C (one atmosphere) ordered, orthorhombic cordierite is stable. Gibbs (1966), in a single crystal refinement of natural cordierite, found a small amount of disorder on the tetrahedral sites but for the puposes of this model cordierite will be considered to be in the fully ordered state. Mirwald (1982) presented evidence of a non-quenchable phase transition in anhydrous cordierite. Dynamic experiments were conducted in a piston cylinder apparatus and discontinuities were found in piston-pressure versus displacement curves, which he interpreted to be the result of a phase transition. He predicted the transition to be at 2.2 kilobars, room temperature and at 8.8 kilobars, 900° C and estimated the volume change of the transition to be AV/V° = 0.0025 (from an experiment at room temperature). The occurrence, position and orientation of H 20 in cordierite has been studied by a number of different authors and methods: Aines and Rossman (1984) - high temperature infrared spectroscopy, Carson et al. (1982) - nuclear magnetic resonance, Armbruster and Bloss (1982) - infrared spectroscopy, Hochella et al. (1979) - high temperature single crystal x-ray diffraction, Goldman et al. (1977) -infrared spectroscopy, Cohen et al. (1977) - x-ray and neutron diffraction and Tsang and Ghose (1972) -nuclear magnetic resonance. All evidence indicates that H 2 0 occurs as molecular H 2 0 and is positioned in the channel cavities. However, it is likely that their is more than one position in the structure. Natural and synthetic cordierites have been found to have more than one mole H 2 0 per unit formula (Leake, 1960; Mirwald et al., 1979) and if the only position is at the centre of the channel cavities (0,0,1/4) then the limit of water content would be one mole per formula. Another possible position for the H 20 molecule could be in the middle of the six-membered rings (0,0,1/2). There is no evidence for hydrogen substitution for silicon (Cohen et al., 1977). Most of the above studies conclude that H 2 0 exists in two orientations: Type I, in which the H-H vector is parallel to the c crystallographic axis and Type II, in which the H-H vector is perpendicular to c (notation of Wood and Nassau, 1967). In both types the H-O-H plane is in the be crystallographic plane. There are some suggestions that the H,0 molecule is present in other orientations. Hochella et al. (1979) suggest from neutron Ap maps that H 20 exists in only one orientation and that Type I and II orientations are vector components of that orientation (H-O-H plane inclined 29° from (100) and the H-H vector 19° from c). Cohen et al. (1977) also calculate neutron Ap maps but interpret the results to represent a space average of four orientations. High temperature infrared spectroscopy at one atmosphere by Aines and Rossman (1984) show that below 200° C H 2 0 is structurally bound and at 400° C 15 H 20 begins to exhibit gas-like characteristics. The spectra obtained indicate that both Types I and II H 20 exist to temperatures of 600° C. Thermodynamic model The existing models of Newton and Wood (1979) and Lonker (1981) assume ideal mixing of the anhydrous and hydrous end-members and equal molar volumes for the solid phase. Newton and Wood use a hydrous end-member with 1.2 moles H 20 and calibrate their model by regressing to the data of Mirwald and Schreyer (1977). Above water contents of about two weight percent (5 kilobars at 600° C) the data are reproduced but at lower contents the model underestimates the data. Lonker uses one mole of H 20 in the hydrous end-member and regresses to data from different pressures. A pressure dependence of cordierite water content was demonstrated and he allowed that this effect could be accounted for by a difference in the end-member volumes, however, he disregards this effect on the basis of published cell volumes of cordierite. They show a negligible volume dependence on H 20 content (Holdaway and Lee, 1977; Dasgupta et al., 1974; Newton, 1972). Lonker presented two models, one regressed from cold seal data (lower pressures) and one from the higher pressure piston cylinder data. Neither model is consistent with all the data and he does not choose between them. Martignole and Sisi (1981) consider H 20 in cordierite to be similar to that in zeolites. They presented a model based on Raoult's law and derived an activity expression for anhydrous cordierite. The data they used to calibrate the model are the low pressure data of Schreyer and Yoder (1964), many of which are suspect due to the pressures and temperatures being outside the "quenchable region" (Medenbach et al., 1980). In order to resolve the inconsistencies of the above models, a new model was developed. The crystal chemical evidence allows for complex models to be considered but the existing data are inadequate over a large enough pressure and temperature range to warrant a model more complex than ideal solid solution. Mirwald et al. (1979) reported water contents of synthetic cordierites of up to 1.3 moles H 20 and Leake (1960) reported contents of natural cordierites of up to 1.6 moles H 20. The hydrous end-member was chosen to have two moles of H 20 in order to cover the possible range of water contents. The equilibrium used to describe H 20 in cordierite is: Mg 2Al 4Si 50 l s + 2H 20 = Mg2Al<Si5018-2H20. - (7) The free energy change of this equilibrium can be expressed as, AGr(P,T) = AG°r(P,T) + RTln k (8) 16 where AG°r(P,T) is the standard state free energy change of the reaction and k is the equilibrium constant If ideal site mixing in a binary system and a pure vapour phase are assumed then, RTlnk = 2RTln[ x j £ g / ( 1 - x g ^ ) ] . (9) Combining equations (8) and (9) and expanding AG°(P,T), T T AGr(P,T) = AH s(P r,T r) + J ACp sdT + (P-PJAV- TAS°S - TJ ACp g/T dT "*r "^r - 2 A GH 2 o( p - T ) + 2 R T l n t * K i ' d - O ^ - <10) Now setting AGr(P,T)= 0, and rearranging to gather unknowns on the left hand side, we have T T AH s(P r,T r) -TAS°S + (P-P r)AV s= - / ACp g dT + TP ACp g/T dT T r T r + 2 A G H 2 0 ( P , T ) - 2 R T l n [ / ( 1 - x ^ ) ] . (11) The experimental data below provide pressures, temperatures and compositions that allow calculation of the right hand side of the equation. When the data are considered as reversed brackets each data point generates a linear inequality (AGr(P,T) < or > 0) that provides a constraint on the values of AH g(P r ,T ), AS°S and AV g. To define a finite region of feasible solutions there must be a minimum of one more datum than there are unknowns, more data can potentially provide additional constraints on this region. Experimental data Several sets of data exist which give the H 2 0 content of Mg-cordierite in equilibrium with H 2 0 as a function of pressure and temperature. The studies and their methods are: 1. Duncan (1982). a. Cold seal apparatus. b. Gravimetric determination of H 2 0 content c. 1 and 2 kilobars, 550 to 750° C. d. Experiments are reversed. 2. Mirwald etal. (1979). a. Cold seal and piston cylinder apparatus. b. Coulometric determination. c. Cold seal - 0.5 to 5 kilobars, 500 to 600° C. Piston cylinder - 3 to 11 kilobars, 500 to 800° C. 3. Mirwald and Schreyer (1977). a. Cold seal and piston cylinder apparatus. b. Coulometric determination. c. Cold seal - 0.5 to 3 kilobars, 500 to 600° C. Piston cylinder - 3 to 10.5 kilobars, 500 to 800° C. 4. Duncan and Greenwood (1977). a. Cold seal apparatus. b. Gravimetric determination. c. 1 and 2 kilobars, 550 to 750° C d. Reversed experiments. 5. Gunter (1977a). a. Apparatus not reported - cold seal (personal communication, Greenwood, 1984). b. H 20 determination technique not reported - gravimetric determination (personal communication, Greenwood, 1984). c. 1 kilobar, 500 and 600° C. 6. Holdaway (1976). a. Cold seal apparatus. b. H 20 determination technique not reported. c. 3 kilobars, 800° C. 7. Newton (1972). a. Piston cylinder and opposed anvil apparatus. b. Estimated from refractive index - calibration from Schreyer and Yoder (1964). c. Piston cylinder - 8 kilobars, 500 and 750° C. Opposed anvil - 10 kilobars, 750° C. 8. Schreyer and Yoder (1964). a. Cold seal piston cylinder apparatus. b. Wet chemistry determination. c. 0.5 to 10.0 kilobars, 500 to 1100° C. There are problems with the experimental and analytical techniques such as rehydration on quench and analytical uncertainty, Lonker (1981) discussed the problems in some detail. The data of Mirwald et al. (1979) and the 2 kilobar data of Duncan (1982) were chosen to calibrate the model. Mirwald et al. provided enough experimental detail to allow some confidence in the results and Duncan (1982) used isobaric and isothermal quenching techniques to demonstrate reversal of equilibrium 18 water contents. Table V lists the data used in the calibration of the model. The other available data were eliminated for the following reasons: 1. Duncan (1982) 1 kilobar data. a. Talc formation is reported although not for specific experiments. Experience in the same chemical system and under similar experimental conditions suggests that talc formation is more likely at 1 kilobar. 2. Mirwald and Schreyer (1977). a. These data are considered to be superceded by Mirwald et al. (1979). b. The data must be estimated by interpolating from a graphic representation. Compositions are not given directly but must be estimated from the given isopleths. 3. Duncan and Greenwood (1977). a. These data are superceded by Duncan (1982). b. The data are presented without full experimental detail. 4. Gunter (1977a). a. The experimental and analytical techniques are not detailed. b. The experimental conditions are outside the quenchable region given by Medenbach et al. (1980). 5. Holdaway (1976). a. The datum is outside the quenchable region of Medenbach et al. (1980). 6. Newton (1972). a. He does not consider the data from the piston cylinder apparatus to be trustworthy. b. It is not clear that H 20 was present as a vapour phase in the opposed anvil experiments. c. The refractive indices quoted are too imprecise to provide precise estimates of H 20 content 7. Schreyer and Yoder (1964). a. The 1 and 2 kilobar experiments are outside the quenchable P-T region. b. The 5 kilobar datum is superceded by Mirwald et al. (1979). c. Other data are not presented in a format useful here. Constraints on the enthalpy, entropy and volume of anhydrous cordierite are available from calorimetric and crystal chemical data. Charlu et al. (1975) present calorimetric data that allows calculation of AfH°(Pr ,Tr), the enthalpy of formation from the elements, to be -9174.406± 3.0 kJ/mol. The entropy for fully ordered cordierite is constrained to lie between 403.338 and 410.869 J/mol-K. (Kelley, 1960) and the volume is constrained to lie between 233.09 and 233.35 cmVmol (Robie et al, 1967). 19 Table V Cordierite hydration data used in the calibration of the cordierite model. P(kilobars)1 T(° C)1 nH20(moles): Mirwald et al. (1979)3 0.5 500 0.42 1.0 500 0.48 I. 0 600 0.42 2.0 500 0.58 2.0 600 0.54 3.0 500 0.64 3.0 600 0.62 4.0 500 0.76 4.0 600 0.64 4.0 700 0.62 5.0 500 0.78 5.0 600 0.68 6.0 600 0.80 6.0 800 0.60 7.0 500 0.84 7.0 600 0.84 7.0 700 0.64 8.0 500 1.08 8.0 600 0.82 8.0 800 0.62 9.0 500 1.20 9.0 600 0.90 9.0 650 0.86 9.0 700 0.74 9.0 800 0.68 10.0 550 1.08 10.0 600 0.92 10.0 750 0.80 10.5 800 0.78 II. 0 500 1.32 11.0 700 0.92 11.0 800 0.82 Duncan (1982)4 - 2kb data 2.0 500 0.68 2.0 600 0.52-0.63 2.0 650 0.47-0.57 2.0 700 0.33-0.44 2.0 • 750 0.18-0.35 'Errors are ± 3% (pressure), ± 10° C (temperature) and ± 10% (composition) for all data. 2The compositions are given as numbers of moles H 20 per formula unit of cordierite (Mg2Al4Si5018-nH20). 3Mirwald et al.'s data are given as 'equilibrium' compositions and pressures and temperatures are estimated from the graphical representation. 4Duncan's data are given as bracketed compositions for the conditions quoted. 20 Fitting procedure The data of Duncan (1982) were reversed and therefore directly represent inequalities. The inequalities can be quantified in terms of free energy where AG r(P,T) > 0 for reactants stable and AG r(P,T) < 0 for products stable. Equilibrium (7) (acrd + 2H 20 = herd) is considered and equation (11) shows the form of the inequalities, with the equal sign being replaced by the appropriate inequality sign. The data of Mirwald et al. (1979) were given as "equilibrium" points although they inherently represent bracketing compositions. Brackets were generated about the given data points in the following manner. Pressures and temperatures were estimated from their graphic representation and adjusted by assuming errors of ± 3% and ± 10° C respectively. Compositions were adjusted by the quoted error of ± 6% and recalculated to mole fractions of the hydrous end-member. The directions of adjustment are dictated by the sign of the slope of the equilibrium and by the relative stability of the assemblages. Figure 3 shows diagrammatically the direction of the pressure, temperature and composition adjustments. The slope of the equilibrium is positive and hydrous cordierite is stable at high pressure in P-T space and in T-x space the slope is negative and hydrous cordierite is stable at low temperature. If the reactants (anhydrous cordierite + 2H 20) are stable then the pressure is decreased, the temperature is increased and the H 20 content is increased (see Figure 3). The opposite adjustments are made for products stable. The data of Duncan (1982) are quoted as reversed brackets and therefore generation of brackets was not required, however, similar adjustments were made to the quoted data with assumed errors of ± 20 bars, ± 10° C and ± 10% in composition. The adjusted experimental data were first tested for internal consistency and then used to calculate internally consistent enthalpies, entropies and volumes for the two end-members. Linear programming techniques were used to solve the systems of linear inequalities represented by equation (11) (see discussion in the Linear Programming Analysis below). The data of Mirwald et al. (1979) were found to be inconsistent if the above errors were used. By relaxing the brackets to ± 10% in composition (pressure and temperature errors remaining the same) internal consistency was achieved. They quoted errors of ± 6% in composition, however this was given as a relative error and errors for individual determinations could have been greater. Several modifications of the model were investigated and are discussed below. The heat capacity of the hydrous end-member was estimated in two ways. First by adding the heat capacity of two zeolitic water (Berman and Brown, 1985) to that of anhydrous cordierite and second by adding two steam. An example of the differences between calculations is shown in Figure 4. The curves shown exhibit minimums at low temperatures and steep negative slopes at lower temperatures. This behaviour is not interpreted to be real but merely to be a numerical artifact of the model, resulting from the Figure 3. Diagrammatic representation of the generation of brackets from the cordierite hydration data. Pen, Terr and Xerr are the errors in pressure, temperature and composition. Note the change in slope between the two diagrams: Both demonstrate hydrous cordierite dehydrating at higher temperatures. 22 TEMPERATURE (deg. C) Figure 4. Isopleths of cordierite, n H Q represents the number of moles H,0 per unit formula. The fine lines are calculated from properties derived from a fit where the heat capacity of the hydrous cordierite end-member was estimated with zeolitic water. The bold lines are calculated from properties derived from another fit where the heat capacity of the end-member was estimated with steam. Also shown are the range of P - T data (dotted line) and the approximate stability field of hydrous cordierite (dashed line), taken from Schreyer and Yoder (1964). 23 change in entropy along the equilibrium. The stability field of cordierite lies above the region where this behaviour is evident (see Figure 4) and the data are reproduced adequately by the model. This behaviour is thus not considered to affect calculations involving stable cordierite. Both models are consistent with the data but they diverge outside the data, especially at lower temperatures. The model using the heat capacity estimated with steam is preferable for the following reasons. Evidence from the high temperature infrared study of Aines and Rossman (1984) indicates that' H 20 exists in cordierite, at least partially, in a gas-like state at temperatures above 400° C (at one atmosphere). The heat capacity of zeolitic water is calculated from calorimetric data for analcime to temperatures of 400° C, whereas the cordierite hydration data starts at 500° C. In addition, calculations with the heat capacity estimate using steam appear to extrapolate more reasonably to lower temperatures. The phase transition suggested by Mirwald (1982) was also tested in the model. The transition was calculated by linearly regressing to the points given in Table 1 of Mirwald (1982); this implies a zero ACp of reaction. A phase transition in hydrous cordierite was assumed to be superimposed on the anhydrous transition and therefore the model was expanded to have two hydration equilibria, one at low pressure and one at high pressure. Volume constraints on the high pressure anhydrous phase were calculated from the low pressure volume constraints using the 0.0025 value for AV/V° given by Mirwald. The entropy of the low temperature phase was constrained to be less than that of the high temperature phase as, in general, the high temperature assemblage of an equilibrium has a greater entropy than that of the low temperature one. With these constraints the compositional errors for Mirwald et al. had to be relaxed to ± 8% to obtain internal consistency, but the resultant volume difference between the two hydrous polymorphs was approximately 8 cm3/mol (approximately 4% difference). This is much larger than the volume changes in other polymorphic phase transitions and is not considered reasonable. In addition, the differences between isopleths of H 20 content calculated for the two stability fields were small and, for simplicity, the transition was ignored. Results The final stages of modelling included testing the data for internal consistency and also the calculation of the final set of thermochemical properties for the phases. The errors in the data of both Duncan (1982) and Mirwald et al. (1979) were ± 3% in pressure, ± 10° C in temperature and ± 10% in composition. These errors were necessary to obtain internal consistency using the model with a single hydration equilibrium and no high pressure polymorphs. The entropy and volume of anhydrous cordierite were fixed at the midpoints of the crystal chemical and calorimetric constraints and different objective functions were used first to minimize then to maximize the P-T slope of the equilibrium. The entropy and 24 volume of the hydrous end-member were then fixed at the midpoints of the ranges calculated and the final fit was made to determine A H r ( P r ,Tr). The resulting changes in enthalpy, entropy and volume for the end-members are given in Table VI. The heat capacity coefficients for anhydrous cordierite are listed in Table IV and those for the hydrous end-member may be calculated by adding the coefficients for two steam (also in Table IV) to those of anhydrous cordierite. Isopleths calculated from equation (10) with the data in Table VI E shown in Figure 5. Also shown, for comparison, are isopleths calculated using the model of Newton and Wood (1979). At pressures above 6 kilobars the two models are in fair agreement but at low pressures Newton and Wood predict H 2 0 contents that are approximately half the values predicted with this model. Table VI Changes in enthalpy, entropy and volume for anhydrous and hydrous cordierite end-members. Hydrous cordierite (Mg 2AL,Si 5 0 i r 2H 2 0 ) minus anhydrous cordierite (MgjALSisOiu). AH s(P r,T r) (J/mol) -563493.8 AS° (J/mol-K) 156.665 A V s (cm 3/mol) 23.066 Orthopyroxene The solid solution behavior in orthopyroxene in the chemical system M ASH has been described recently by Gasparik and Newton (1984) where they used a Tschermak's exchange between enstatite ( M g 2 S i 2 0 6 ) and Mg-Tschermaks ( M g A l 2 S i 0 6 ). The aluminum content is a function of pressure, temperature and stable assemblage defined by the two equilibria, 1 Enstatite + 1 Spinel = 1 Mg-Tschermaks + 1 Forsterite (12) 1 Enstatite 4- 1 Mg-Tschermaks = 1 Pyrope. (13) Gasparik and Newton (1984) used their data plus data from Perkins et al. (1981) and Danckwerth and Newton (1978) to calibrate their model. They assumed constant heat capacities, a linear volume of solution and also included expansivities and compressibilities. Disordering phenomena in spinel or orthopyroxene were not explicitly included in their model. Gasparik and Newton regressed the data from each stability field to obtain AH° 9 7 o, AS° 9 7o and AV° 2 9 8 for equilibria (12) and (13). The functions obtained give the equilibrium aluminum content of orthopyroxene as a function of pressure, temperature and stable 25 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 TEMPERATURE (deg. C) Figure 5. Water content of Mg-cordierite in equilibrium with H 2 0 as a function of pressure and temperature. The isopleths are labelled with the number of moles of H 2 0 (n) per unit formula. Bold lines are the isopleths calculated from the data in Table VI and the fine lines are isopleths calculated using the model of Newton and Wood (1979). 26 assemblage. The free energy of orthopyroxene was calculated by, AGopX(p'T> = * G°CTx( p- T> + R T l n xh5 x Ordering of aluminum in orthopyroxene has been investigated by Ganguly and Ghose (1979) in a crystallographic study of synthetic and natural orthopyroxenes. They found the tetrahedral aluminum to be almost completely ordered into one of the tetrahedral sites and the octahedral aluminum to be partially ordered into the Ml site. This allows more complex modelling but was not considered in the calculation of orthopyroxene free energy. . Solid solution towards A1203 is known (Roy et al., 1953; Navrotsky and Kleppa, 1967), however, Roy et al. and Seifert (1974) found no evidence of solid solution below 1100° C. In addition, Chernosky (1974), in his related study, found no evidence of solid solution. The same chemical system, phases and conditions were analyzed here and therefore spinel was considered to be on composition. The effect of variable disorder in spinel was not considered in the analysis for the following reasons: 1. The degree of disorder is not known accurately as a function of pressure and temperature. 2. The phase equilibria data used here were not constraining enough to warrant the use of a disordering The calculations below estimate a possible contribution of variable disorder to the free energy of spinel. O'Neill and Navrotsky (1984) used the relation, to describe the free energy of disorder. AG c c l is the free energy of cation disorder, AG^ is the non-configurational free energy and S is the configurational entropy. Equation (14) may be expanded to, Spinel model. AGc.d. = A G d - T S c (14) A Gc.d. = A H d - T ( S c + Sd)' (15) where AH^ and S^  are the enthalpy and entropy of disorder. If the functions for AFLj and S^  from O'Neill and Navrotsky (1984) and S from O'Neill and Navrotsky (1983) are used (15) expands to, A G c d = ( a A - afi)x + 0x 2Tf -R[ xlnx + (l-x)ln(l-x) + xln(x/2) + (2-x)ln( l-(x/2))] + (aA~ afi)x} (16) 27 The parameters g are empirically determined "site preference enthalpies" for cations corresponding to the general formula AB204, /3 is a constant for the type of spinel considered (2-3 here, notation of Navrotsky and Kleppa, 1967) and are "site entropies" analogous to the site preference enthalpies (see Navrotsky and Kleppa, 1967). Values for these parameters were given in O'Neill and Navrotsky (1984). The variable x is the degree of disorder indicated in the formula Aj_ xB x(A xB2_ x)0 4, where A and B represent the octahedral and tetrahedral sites. Unfortunately the degree of disorder, x, is not known as a function of pressure and temperature and could not be measured in the products of the experiments due to small grain size. Wood and Holloway (1984) estimated x as a function of temperature by assuming a constant enthalpy of disorder (AHc ^ ) of 83.68 kJ/mol in the relation, -AH c d/RT = In [ xV( (l-x)(2-x))]. (17) The free energy contribution from disorder was calculated, from equations (16) and (17), to be -246 J/mol at 600° C and -4868 J/mol at 1600° C, the approximate range of temperatures considered in this analysis. If the spinel in the experiments reached equilibrium states of disorder then the free energy effects can be significant Wood and Holloway (1984) showed that the phase equilibria data cannot be fit using this model. Chlorite Mg-chlorite has a variable content of aluminum and evidence from natural chlorites suggest that the range of solution is between Mg^Al^Sij^O^OH^ and Mg^Alj.jSi^O^OHX (Foster, 1962). In order to encompass the range of composition, the end-members Mg6Si4Oi0(OH)8 (Chls) and Mg4Al4Si2O10(OH)8 (Coph) were chosen. Crystal chemical evidence so far obtained is not sufficient to define rigorously the solution characteristics so a Tschermak's exchange was assumed. If ideal solution is assumed the free energy of chlorite can be expressed as, Gchl(P,T) = (l-x^ h)G c h l s(P,T) + x^ hG c o p h(P,T) ' + 2RT[ x ^ h l n x ^ h + (1- x ^ h ) l n ( l - x g £ h ) ]. (18) Gckjs(P,T) and ^ ^^(P.T) are the free energies of the end-members at pressure and temperature and chl chl xcoph *s t^ie m o ' e fracuon °f corundophyllite in chlorite. For the clinochlore composition x^ ^  is 0.5 c h l and for the composition considered here (Mg 4. 75Al 2.jSi2 .7 5Oio(OH) 8), x ^ ^ is 0.625. The reason for doubling the configurational entropy term is that there are two atoms of aluminum substituting on the 28 tetrahedral sites (coupled substitution with octahedral aluminum). The heat capacities of the end-members were estimated by adding or subtracting the heat capacities of the appropriate oxides to or from the heat capacity of clinochlore. Berman and Brown (1985) used the calorimetric data of Henderson et al. (1983), for a natural chlorite close to the clinochlore compositiont, to calculate the heat capacity coefficients for clinochlore (adjustments were made for the compositional differences). There is possible disordering on the tetrahedral and octahedral sites in the 2:1 layer and also on the octahedral sites of the interlayer. Stacking disorder is also possible. Bailey and Brown (1962) discussed the crystal chemistry of chlorite and gave a geometric basis for twelve polytypes. They indicated that only three of these polytypes have been found naturally with the lib polytype being the most common. Mixing of polytypes will result in stacking disorder and this has been investigated by Spinnler et al. (1984). They used single crystal x- ray methods, high resolution transmission electron microscopy and electron diffraction in a study of a natural chlorite close to the clinochlore composition. The stacking order observed was nearly completely ordered although some disorder was noted. None of the disordering phenomena in chlorite are well understood nor were they measured in the synthetic chlorite used in this study and so were not considered in the modelling done here. Linear Programming Analysis Linear programming was chosen as the mathematical technique to analyze the data, as opposed to the more widely used regression analysis, because it is compatible with the nature of phase equilibria data. Phase equilibria data provide information about the relative stability of assemblages (AG r< > 0) but give little statistical information about the distance from the equilibrium. Linear programming was introduced into the geologic literature by Gordon (1973; 1977) and since then a number of studies have utilized this technique (for example: Day and Halbach, 1979; Day and Kumin, 1980; Halbach and Chatterjee, 1982; 1984; Berman and Brown, 1984; Day et al., 1985). Phase equilibria data The data retrieved from the literature for equilibria (1) through (5) are listed in Table VII, only experiments that demonstrated reversal are included. The nominal pressures and temperatures were adjusted to the limits allowed by the quoted or estimated errors in the manner described in the cordierite analysis above. These constraints were further relaxed using estimates for the bracketing compositions of orthopyroxene and chlorite. For orthopyroxene the minimum and maximum aluminum contents were 29 Table VII Phase equilibria data for equilibria (1) through (5) Study P(kbars) T(°C) Stable assemblage (1) Chl = Cd+Fo+Sp + H 2Q This study Mg 4. 7 5Al 2. 5Si 2. 7 5O 1 0(OH) 8 Chernosky (1974) Mg 5Al 2Si 3O 1 0(OH) 8 (2) Chl = Opx + Fo+Sp + H 2Q Jenkins (1981) Staudigel and Schreyer (1977) Fawcett and Yoder (1966) (3) Chl = Py + Fo+Sp + H 2Q Staudigel and Schreyer (1977) (4) Cd + Fo = Opx + Sp Herzberg (1983) 0.50C025)1 0.50(.020) 1.00(.025) 1.00(.030) 2.00(.040) 2.00(.030) 0.500(.020) 0.500(.020) 1.000(.020) 1.000(.020) 2.000(.040) 2.000(.040) 3.000(.060) 3.000(.060) 10.000(300) 10.000(300) 14.000(.420) 14.000(.420) 11.000(— 2) 11.000(—) 15.000(—) 15.000(~) 18.000(—) 18.000(~) 5.000(150) 10.000(.100) lO.OOO(.lOO) 22.000(— 2) 22.000(~) 25.000(—) 25.000(~) 30.000(~) 30.000(—) 35.000(—) 35.000(~) 40.000(~) 1.750(.100) 2.200(.100) 1.500(.100) 605(5)' 640(5) 644(5) 670(4) 690(10) 704(5) 576(5) 635(5) 636(5) 662(5) 694(5) 710(5) 726(5) 750(5) 815(10) 825(10) 850(10) 860(10) 825(20) 840(20) 845(20) 850(20) 875(20) 890(20) 800(5) 825(10) 837(10) 890(20) 900(20) 890(20) 900(20) 875(20) 880(20) 870(20) 880(20) 800(20) 1150(25) 1150(25) 1200(25) Chl Cd+Fo+Sp Chl Cd + Fo+Sp Chl Cd + Fo+Sp Chl Cd+Fo+Sp Chl Cd+Fo + Sp Chl Cd + Fo+Sp Chl Cd + Fo+Sp Chl Opx + Fo+Sp Chl Opx + Fo + Sp Chl Opx + Fo+Sp Chl Opx + Fo+Sp Chl Opx + Fo + Sp Opx + Fo+Sp Chl Opx + Fo + Sp Chl Py + Fo+Sp Chl Py + Fo+Sp Chl Py + Fo+Sp Chl Py + Fo+Sp Chl F o+Cd Opx + Sp Fo+Cd 30 Table VII (continued) Study P(kbars) T(°C) Stable assemblage Herzberg (1983) (continued) Seifert (1974) Fawcett and Yoder (1966) (5) Opx + Sp = Py + Fo Gasparik and Newton (1984) Perkins et al. (1981) Danckwerth and Newton (1978) 2.200(100) 1.2000100) 1.500(.100) 3.000(.200) 3.025(.200) 2.800(.200) 3.000(.200) 2.500(.200) 2.800(.100) 3.100(.063) 3.300(.069) 21.960(2%)3 21.340(2%) 29.700(2%) 29.250(2%) 26.440(2%)4 25.620(2%) 24.570(2%) 21.840(2%) 20.020(2%) 22.890(2%) 20.380(2%) 20.500(2%) 25.160(2%) 20.000(2%) 21.480(2%) 18.800(2%) 18.200(2%) 19.050(2%) 18.500(2%) 19.500(2%) 19.000(2%) 20.000(2%) 19.500(2%) 20.500(2%) 20.000(2%) 1200(25) 1300(25) 1300(25) 850(15) 905(15) 1000(15) 1000(15) 1100(15) 1100(15) 790(5) 780(5) 1200(15) 1200(15) 1600(15) 1600(15) 1465(15) 1435(15) 1405(15) 1240(15) 1100(15) 1260(15) 1110(15) 1100(15) 1425(15) 1085(15) 1145(15) 900(10) 900(10) 950(10) 950(10) 1000(10) 1000(10) 1050(10) 1050(10) 1100(10) 1100(10) Opx + Sp Fo+Cd Opx+Sp Fo+Cd Opx + Sp Fo+Cd Opx + Sp Fo+Cd Opx + Sp Fo+Cd Opx + Sp Py + Fo Opx + Sp Py + Fo Opx + Sp Py + Fo Py + Fo Opx + Sp Opx + Sp Opx + Sp Py + Fo Opx + Sp Py + Fo Py+Fo Opx + Sp Py + Fo Py + Fo Opx + Sp Py + Fo Opx + Sp Py + Fo Opx + Sp Py + Fo Opx + Sp Py + Fo Opx + Sp 'Numbers in brackets represent errors used to adjust the pressures and temperatures for the linear programming analysis. 'Pressures given by Staudigel and Schreyer (1977) - corrections and adjustments are explained in the text Pressures have been corrected for friction using the functions of Gasparik and Newton (1984). 'Pressures have been corrected for friction using the function of Perkins et al. (1981). 31 assumed to be that of the pyroxene used in the starting materials (usually enstatite) and that calculated by the model of Gasparik and Newton (1984). The chlorite compositions for equilibria (2) and (3) were bracketed by the composition of the starting material (clinochlore) and the composition given by Jenkins (1981), Mg4.88Al2.24Si2.88 0 1o(OH)8. This was given as the approximate composition of chlorite at the breakdown to orthopyroxene, forsterite and spinel at 14 kilobars (850° C). Specific adjustments to the data for each equilibrium are outlined below: Equilibrium (1): Chl = Cd + Fo + Sp + H 20 1. Fawcett and Yoder (1966), Chernosky (1974). Quoted pressure and temperature errors were used and the chorite composition was assumed to be clinochlore. 2. This study. Quoted pressure and temperature errors were used and the chlorite composition was x c h l . =0.625. coph Equilibrium (2): Chl = Opx + Fo + Sp + H 20 1. Fawcett and Yoder (1966). Quoted pressure and temperature errors were used. The orthopyroxene composition was bracketed between enstatite and the calculated equilibrium composition and chlorite between clinochlore and that of Jenkins. 2. Staudigel and Schreyer (1977). Temperature errors of ± 20° C were used as the quoted temperatures were not adjusted for the pressure effect on the emf of the thermocouple. The quoted temperature error was ±10°C. Pressures were corrected using the function of Gasparik and Newton (1984) for a talc plus soft glass assembly. Quoted pressures are nominal and the pressure medium used was talc plus boron nitride (W. Schreyer, personal communication). An error of ± 5 percent was assumed after the correction. The orthopyroxene composition was bracketed between enstatite and the calculated equilibrium composition and the chlorite composition between clinochlore and that of Jenkins. 3. Jenkins (1981). Quoted pressure and temperature errors were used. The orthopyroxene composition was assumed to be the calculated equilibrium composition. The composition of the orthopyroxene in the starting materials was 10 mole percent Mg-Tschermaks which is close to the calculated compositions. Chlorite composition was bracketed between clinochlore (starting material) and that of Jenkins. Equilibrium (3): Chl = Py + Fo + Sp + H 20 1. Staudigel and Schreyer (1977). See above. 32 Equilibrium (4): Cd + Fo = Opx + Sp 1. Fawcett and Yoder (1966), Seifert (1971). Quoted pressure and temperature errors were used. The orthopyroxene composition was bracketed between enstatite, the starting material, and the calculated equilibrium composition. Hydrated cordierite was assumed. 2. Herzberg (1983). Quoted pressure and temperature errors were used. The orthopyroxene composition was bracketed between 20 mole percent Mg-Tschermaks (starting material) and the calculated equilibrium composition. Anhydrous cordierite was assumed as the experiments were run in the absence of H 20. Equilibrium (5): Opx + Sp = Py + Fo 1. Danckwerth and Newton (1979), Perkins et al. (1981) and Gasparik and Newton (1984). Quoted pressure and temperature errors were used. The orthopyroxene compositions were assumed to be the calculated equilibrium compositions as the compositions of the pyroxenes used in the starting materials were close to the calculated ones. Constraints The entropies and volumes for phases other than chlorite were constrained to the properties derived by Berman (1985). The properties he derived are consistent with phase equilibria and calorimetric data in the larger chemical system K 2 0 - N a 2 0 - M g O - F e O - F e 2 0 3 - C a O - A l 2 0 3 - S i 0 2 - H 2 0 - C 0 2 . There are two points to note: The entropies of cordierite and spinel include small contributions for disorder, approximately 8 J/mol and 3 J/mol respectively. These adjustments allow the calculated enthalpies of cordierite and spinel to agree more closely with calorimetric determinations. Disorder in natural cordierite has been documented by Gibbs (1966). The contribution for disorder in spinel was estimated by Gasparik and Newton (1984) and has been successfully used by Harris and Holland (1984) and Berman (1985). chl The properties of chlorite were constrained in two ways. At the clinochlore composition ( x^Qpjj = 0.5) the solution was constrained to the properties derived for clinochlore by Berman (1985). Constraints were also estimated for the volumes and entropies of the two end-members. There are some data for the volumes of Mg-chlorite as a function of Al-content and they are listed in Table VIII. Most of the volume data are for synthetic chlorites of the clinochlore composition. There are data for cell parameters of natural chlorites (eg. Albee, 1962; Foster, 1962; Brindley and Gillery, 1956) but only for the variation of d(001) with Al-content (see Figure 2) in Fe-Mg chlorites, and of d(060) with Fe-Mg ratio. These data suggest a larger dependence of volume on Al-content than the limited data on synthetic chlorites indicate (see Figure 33 Table VIII Volumes of Mg-chlorites Study xchl xcoph V(cmVmol) Fawcett and Yoder (1966) 0.5 208.16 Bird and Fawcett (1973) 0.5 211.74 Chernosky (1974) 0.5 211.535 McOnie et al. (1975) 0.5 209.59 Staudigel and Schreyer (1977) 0.5 210.49 Chernosky (1978) 0.5 211.52 Henderson et al. (1983) 0.5 209.8 Jenkins and Chernosky (1985) 0.5 210.98 0.5 210.82 0.5 210.76 0.6 210.43 0.7 210.32 This study 0.625 209.515 2), but the effect cannot be fully evaluated due to the lack of volume data. A range of end-member volumes were calculated as follows. All of the data in Table VIII were linearly regressed to determine a slope of -2.68 for the volume of solution. This is considered to represent the minimum difference of the end-member volumes if ideal solution is assumed. A maximum difference was estimated by using the two chl volumes that give the steepest slope: Bird and Fawcett (1975), ^ c o ^ =0.5, V = 211.74 cmVmol and this chl study, xcoph = ^2-'' V = 209.52 cm3/mol. The slope calculated was -17.80. If a volume of clinochlore of 209.818 (Berman, 1985) was assumed, then the volume ranges of the end-members are: 210.5-216.0 cm3/mol for the aluminum free end-member and 203.0-209.0 cm3/mol for the other end-member. The entropies of the end-members were estimated using the method of Helgeson et al. (1978). When the minimum AV (2.68 cm3/mol) of the two end-members and a clinochlore entropy of 429.77 J/mol-K were used then the entropies of the two end-members were calculated to be 439.94 J/mol-K (chls) and 419.60 J/mol-K (coph) (AS = 20.34 J/mol-K). If the maximum AV (17.80 cmVmol) was assumed then the entropies were calculated to be 447.68 J/mol-K (chls) and 411.86 J/mol-K (coph) (AS = 35.82 J/mol-K). Fitting procedure The above data and constraints were used to calculate possible ranges of values for the thermochemical properties of the chlorite solution allowed by the phase equilibria data included in this study. This was accomplished, after fixing the volume of clinochlore to be that of Berman (1985) (209.818 34 cmVmol), by using different objective functions in the linear programming routines. The enthalpies of enstatite, forsterite, pyrope and H 2 0 were fixed to the values calculated by Berman (1985). The range of entropy for clinochlore was calculated to be between approximately 420 J/mol-K and 480 J/mol-K. An entropy of clinochlore of 429.77 J/mol-K is preferred as this is the value calculated from a much larger data set (Berman 1985). Henderson et al. (1983) calorimetrically determined the entropy of clinochlore to be 397.3 J/mol-K, a difference of 32.5 J/mol-K. Disorder on the tetrahedral and octahedral sites can account for the apparent discrepancy. At the clinochlore composition one of four tetrahedral sites and one of six octahedral sites can be assumed to be occupied with aluminum. If stacking disorder and excess entropy are ignored then the maximum configurational entropy of clinochlore is -6R[ (l/6)ln(l/6) + (5/6)ln(5/6) ] -4R[ (l/4)ln(l/4) + (3/4)ln(3/4) ] = 41.18 J/mol-K. This would appear to indicate that the difference between the calculated entropy from the phase equilibria data and the calorimetrically determined entropy are for a nearly fully disordered phase and a nearly fully ordered phase respectively. In order to see if the phase equilibria data constrained the properties of the chlorite end-members the volume and entropy constraints on the end-members were removed and several calculations were made. The entropy and volume of clinochlore were fixed at the values shown above (429.77 J/mol-K and 209.818 cmVmol) and the ranges of the entropies and volumes of the end-members were determined No significant bounds were found. The entropies of the end-members ranged from 0.0 to twice that of clinochlore (860 J/mol-K) and the volumes were only loosely constrained to within approximately 60 cmVmol. This is not surprising as the free energy constraints on the solution are at or near the middle of the compositional range considered. The enthalpies of cordierite, spinel and chlorite were then determined by first constraining the enthalpies of cordierite and spinel to those derived by Berman (1985). When these constraints were added the system of inequalities became inconsistent By increasing the enthalpy of spinel by approximately 400 J/mol to -2303.32 kJ/mol all constraints were satisfied. There are two reasons that explain why this was necessary: The bracketing composition of the higher aluminum chlorite used in Berman's study was chl Mg 4 . ,Al i 4 Si i , 0 1 o (OH), ( xooph _0-6), higher than the composition used here; he used a different activity model for describing the variable chlorite composition - clinochlore was used as the standard state and the activity of clinochlore in the higher aluminum chlorite was assumed to be 0.8. The adjustment in the enthalpy of spinel allowed better agreement with the measured values of - 2302.00 ± 2.70 kJ/mol (Shearer and Kleppa, 1973) and -2299.71+ 1.53 kJ/mol (Charlu et al, 1975). 35 Results The resulting enthalpies, entropies and volumes of the phases determined here are listed in Table IX. Included are the estimated properties for the two end-members of the chlorite solution. The entropies of the end-members were taken to be the midpoints of the ranges estimated above. This allowed the calculated volumes to be close to. the midpoints of the estimated ranges. Figure 6 shows equilibrium (1) calculated from the data in Tables IV and IX for the clinochlore composition and for the chlorite composition used in the experiments in this study. Also shown are the most constraining data from Chernosky (1974) and this study, all data have been adjusted by quoted errors in pressure and temperature. The displacement for this difference in composition is approximately 8° C at 2 kilobars. The set of all five equilibria considered in this study are shown in Figure 7. The equilibria are calculated assuming excess H 20 and with variable compositions of cordierite and orthopyroxene. The chl chlorite composition used in the calculation was x ^ = 0.6, the composition indicated in Frost (1975). He studied the contact metamorphism of an ultramafic package in the Paddy-Go-Easy Pass area of Washington. This allowed him to track the composition of Mg-rich chlorites to their breakdown to orthopyroxene, forsterite and spinel. He found the aluminum content of chlorite to increase as breakdown chl was approached and the final composition to be x jj = 0.6. This might represent the equilibrium composition of Mg-chlorite at breakdown more accurately than clinochlore. There are other equilibria generated from the two invariant points but for clarity they are not shown. 36 Table IX Calculated enthalpies of formation from the elements, third law entropies and molar volumes for phases and species used in this study. Phase Clinochlore Mg 5Al 2Si 3O 1 0(OH) 8 Chls Mg 6Si 4O 1 0(OH) 8 Corundophyllite Mg,Al«Si,0,o(OH), Cordierite Mg 4Al 4Si 2O 1 0(OH) 8 Enstatite Mg 2Si 20 6 Forsterite Mg 2Si0 4 Pyrope Mg 3Al 2Si 30 1 2 Spinel MgAl 20 4 Water H 20(liq) A fH"(P r ,Tr) (J/mol) -8921085.4 -8890543.1 -8951627.7 -9162360.3 -3092948.5 -2176634.6 -6290010.0 -2303323.8 -285830.0 S°(Pr ,Tr) (J/mol-K) 429.77 432.28 404.20 418.50 132.34 94.01 267.27 83.67 69.92 V (cm3/mol) 209.82 216.08 203.56 233.09 62.68 43.80 113.18 39.74 37 400 450 500 550 600 650 700 750 800 TEMPERATURE (deg. C) Figure 6. The equilibrium Chlorite = Cordierite + Forsterite + Spinel + H 20. The curves chl are labelled with x jj, 0.5 represents the clinochlore composition and 0.625 is the composition used in the experiments of this study. Solid symbols are reversals for the low temperature side of the equilibria and the open symbols are for the high temperature side. The triangles are data from Chernosky (1974) and the squares are data from this study. 38 0 200 400 600 800 1000 1200 1400 1600 TEMPERATURE (deg. C) Figure 7. The upper thermal stability of Mg-chlorite. Equilibrium compositions of cordierite and orthopyroxene are calculated as a function of pressure, temperature and coexisting assemblage by the models of this study (cordierite) and Gasparik and Newton (1984) (orthopyroxene). The composition of chl chlorite used is x^" h = 0.6. Other equilibria generated from the two invariant points are not shown. 39 CONCLUSIONS The upper thermal stability of Mg-chlorite at a given pressure is dependent on the breakdown assemblage and the composition of chlorite. With increasing pressure the breakdown assemblage changes to include cordierite, orthopyroxene and then pyrope (all present with forsterite, spinel and H 2 0). Some of these phases exhibit compositional variations and/or ordering phenomena. The variable H 2 0 content in cordierite was described with a model using ideal solution between the end-members M g 2 A l 4 S i 5 0 1 8 and Mg 2Al 4 Sij0 1 8-2H 2 0. Orthopyroxene aluminum content was also described by a model employing ideal solution between the end-members Mg 2Si 2 0 6 and MgAl 2 S i 0 6 . The variable composition of chlorite was modelled assuming ideal solution between the end-members Mg 6Si 4O 1 0(OH) 8 and Mg 4Al 4Si 2O 1 0(OH) 8. Disordering phenomena in cordierite and spinel were accounted for by adding small entropies of disorder to the third law entropies and ordering of A l on the octahedral sites in orthopyroxene was not accounted for. Differences between the calorimetrically determined entropy for clinochlore and that calculated from phase equilibria data can be accounted for by entropies of disorder on the tetrahedral and octahedral sites. The above assumptions and estimations were combined with new and existing data to derive internally consistent thermochemical properties for the phases considered. The results indicated a small displacement of high entropy reactions such as the breakdown equilibria of chlorite as a result of variable aluminum contents of Mg-chlorite. Displacement of the low pressure breakdown of chlorite due to variable Al-content of chlorite was not resolved experimentally. There are not enough data available to be able to define the solution mechanisms operating in Mg-chlorites and the data were able to be fit assuming ideal solution and a Tschermak's exchange. Evidence from natural systems indicates the composition of chl Mg-chlorite at the breakdown to orthopyroxene, forsterite and spinel is ^= 0.6. The accumulation of more crystal chemical, calorimetric, spectroscopic and phase equilibria data will allow more precise modelling of the solid solution and disordering behaviours in chlorite. Crystal chemical data will help constrain the volume of solution and provide information on the substitution mechanisms that occur, as well as determination of long range stacking orders. Studies utilizing high resolution transmission electron microscopy might allow determination of short range stacking disorder. Calorimetric studies can provide direct measurements of the thermochemical effects of solid solution and also of disorder and spectroscopic data might indicate the distribution of cations in both the octahedral and tetrahedral sites. 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