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The Fe-Mg solution properties of olivine, enstatite, anthophyllite and talc, from ion-exchange experiments… Bartholomew, Paul Richard 1984

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THE Fe-Mg SOLUTION PROPERTIES OF OLIVINE, ENSTATITE, ANTHOPHYLLITE AND TALC, FROM ION-EXCHANGE EXPERIMENTS WITH AQUEOUS CHLORIDE SOLUTIONS By PAUL RICHARD BARTHOLOMEW B.S., The University of Minnesota, 1976 M.Sc.'j The University of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES THE DEPARTMENT OF GEOLOGICAL SCIENCES We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1984 ©Paul Richard Bartholomew, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) Abstract Ion-exchange e q u i l i b r i a between a 2molal aqueous Mg-Fe chloride solution and synthetic o l i v i n e s , orthopyroxenes, orthoamphiboles and t a l c s have been experimentally bracketed between 450° and 800°C and between 1 and 4kb. Additional experiments at lower chloride m o l a l i t i e s reveal that the d i s t r i b u t i o n c o e f f i c i e n t measured i s dependent upon chloride concentration. Thermodynamic modelling of the chloride s o l u t i o n , assuming ideal mixing of Mg and Fe species, q u a l i t a t i v e l y reproduces this behavior i f the Mg and Fe species have contrasting d i s s o c i a t i o n constants. Internally consistent thermodynamic properties of a l l four minerals and the 'delta' properties of a hypothetical associated e l e c t r o l y t e solution are calculated through a combination of linear programming and least-squares optimization while simultaneously considering constraints provided by calorimetry, net-transfer e q u i l i b r i a and other ion-exchange data. Adequate correspondence between thermodynamic model and the data cannot be attained'without allowing the mixing of Mg and Fe.in the chloride solution to be non-ideal. Qualitative constraints on the chloride 'excess' properties allow a preliminary estimate of the s o l i d solution properties to be made. A l l s o l i d solutions are modelled with a symmetric Margules formulation. The resulting o l i v i n e • function has a value near 7kJ at 400°C and drops asymptotically toward zero at high temperatures. The orthopyroxene Wr is approximately zero at 400°C and drops toward -3kJ at high temperatures. A 'microscopic' orthopyroxene solution model is formulated to be simultaneously consistent with t h i s bulk excess free energy and with measured M1-M2 s i t e d i s t r i b u t i o n s . The single WQ value (0.58kJ) calculated for the anthophyllite s o l i d solution i s q u a l i t a t i v e l y consistent with fractionation of Fe into M4. The t a l c s o l i d solution cannot be constrained to be d i f f e r e n t from ideal by the data presented here. At present, ion-exchange experiments with Mg-Fe chloride solutions can only be used to compare mineral properties due to uncertainties in d i s s o c i a t i o n constants and 'excess' properties for the aqueous so l u t i o n . The role of such uncertainties in the data analysis indicates that s o l i d solution properties derived from previous aqueous chloride ion-exchange experiments must be considered suspect u n t i l the properties of each pertinent aqueous e l e c t r o l y t e solution have been examined. Table of Contents Chapter Page Abstract i i L i s t of Tables vi L i s t of Figures . . . v i i L i s t of Plates x Acknowledgements ...xi I. Ion-Exchange Equilibrium with Mg-Fe Olivine and Modelling of the Aqueous Solution 1 Introduction 1 Experimental Techniques 3 Data Analysis ....13 Discussion 48 I I . Application to Orthopyroxene, Orthoamphibole and Talc and Comprehensive Analysis 53 Introduction 53 Experimental Techniques 56 Data Analysis 64 Discussion 93 Conclusions 99 References 101 III . APPENDICES 115 APPENDIX A: Oxide Mixes ..115 APPENDIX B: Aqueous Analyses 118 APPENDIX C: Electron Microprobe Analyses ...123 APPENDIX D: High Accuracy Powder XRD -..132 APPENDIX E: Transmitted Electron Microscopy 137 APPENDIX F: Orthoamphibole Synthesis and Characterization 144 iv APPENDIX G: The Mg-Fe Orthopyroxene Solution 1 68 v L i s t of Tables Table 1.1. Ion-exchange run data 14 Table 1.2. F i t parameters for equation (3) for several aqueous chlorides 23 Table 1.3. Isothermal-isobaric regression results for the ion-exchange reaction and the stoichiometric o l i v i n e solution model 38 Table 1.4. Regressed f i t parameters for the ion-exchange reaction and the stoichiometric s o l i d solution model 42 Table 1.5. Olivine c e l l parameters derived from powder XRD peaks in the 40° to 75°20 range 43 Table II.1 Orthoamphibole d0k0 values measured for ion-exchange run products 62 Table II.2 Talc rf003 values measured for ion-exchange run products 64 Table II.3. Ion-exchange run data 65 * Table II.4. LnKD values calculated for a l l o l i v i n e + 2m chloride ion-exchange experiments 69 Table II.5 Endmember thermodynamic properties for Model 1 75 Table II.6 Model 1 Margules parameters 76 Table II.7 Endmember thermodynamic properties for Model 2 85 Table II.8 Model 2 Margules parameters 86 Table B1 . Quench pH measurements 119 Table C1 . Summary of microprobe analyses 127 Table F1. Experimental parameters for orthoamphibole syntheses 150 Table F2. Orthoamphibole c e l l parameters derived from least squares refinement of powder XRD data 151 Table G1 . O r i g i n a l and adjusted values of l n KD 1 2 173 Table G2. F i t parameters resulting from successive p a r t i a l regression of the speciation model to the orthopyroxene data 192 vi L i s t of Figures Figure 1.1 Comparison of standard and p a r t i c l e analyses for cases in which both techniques were applied to samples of the same product o l i v i n e s 12 Figure 1.2 Compositional changes measured for ion-exchange experiments at 600°C, 2kb 17 Figure 1.3 Theoretical trends of lnK^ vs Xf Q given that the aqueous f l u i d behaves as a thermodynamically ideal solution of the chloride endmembers 18 Figure 1.4 Common logarithm of aqueous chloride dissociation constants at 2kb 22 Figure 1.5 The effect of variations in logKF g on lnKD as predicted by the f i r s t - d i s s o c i a t i o n model for the hypothetical case in which the o l i v i n e s o l i d solution i s ideal 29 Figure 1.6 lnKD vs mT for i s o t h e r m a l - i s o b a r i c - i s o X ^ subsets of the ion-exchange experiments 33 Figure 1.7 A compilation of the most recent and most comprehensive measurements of and Margules solution models for Mg-Fe o l i v i n e s 39 Figure 1.8 lnKD vs X^Q: 2m chloride ion-exchange data and curves calculated with Model B combined with the f i r s t - d i s s o c i a t i o n model with the same values of T, P and mT 45 Figure 1.9 WQ and WH calculated using the f i t parameters l i s t e d under Model B in table 4 51 Figure I I . 1 Values of d0ll0 measured for the synthetic orthoamphibole starting materials 61 Figure II.2 Measured values of ta l c d003 and the linear c a l i b r a t i o n curve f i t to the synthetic star t i n g materials produced in the present study 63 * Figure II.3 Comparison of o l i v i n e lnKQ data with curves calculated with Model 1 thermodynamic parameters 77 v i i * Figure II.4 Comparison of orthopyroxene lnKD data with curves calculated with Model 1 thermodynamic parameters 79 * Figure II.5 Comparison of orthoamphibole lnK^ data with curves calculated with Model 1 thermodynamic parameters 80 * Figure II.6 Comparison of t a l c lnKD data with curves calculated with Model 1 thermodynamic parameters 81 Figure II.7 Comparison of the four Model 1 WQ functions 82 * Figure II.8 Comparison of o l i v i n e lnKD data with curves calculated with Model 2 thermodynamic parameters 87 * Figure II.9 Comparison of orthopyroxene lnKD data with curves calculated with Model 2 thermodynamic parameters. 89 * Figure 11.10 Comparison of orthoamphibole lnK^ data with curves calculated with Model 2 thermodynamic parameters 90 * Figure 11.11 Comparison of ta l c lnKD data with curves calculated with Model 2 thermodynamic parameters 91 Figure 11.12 Comparison of the four Model 2 WQ functions 92 Figure C1. Empirical c a l i b r a t i o n curve for p a r t i c l e analysis correction 126 Figure F1. Orthoamphibole unit c e l l parameters 153 Figure G1. Uncertainties inherent in measurement of orthopyroxene s i t e occupancies from Mossbauer spectra of the products of disordering experiments 171 Figure G2. Corrected l n KD 1 2 values plotted versus XE n > The f i l l e d symbols represent data from Saxena and Ghose(l970) 175 Figure G3. LnKD 1 2 curves calculated from the v i i i speciation model formulation for sample values of AGL, AGg, and WgPec 189 Figure G4. Comparison of macroscopic data, formulated as Margules parameters, with equivalents calculated at XEn=0.5 from the orthopyroxene speciation model 193 Figure G5. Comparison of lnKD 12 data from Saxena and Ghose(l970) with l n KD 1 2 curves calculated from the orthopyroxene speciation model 194 Figure G6. Gg^l k (equation (G18)) and i t s components calculated as a function of temperature for the orthopyroxene speciation model 195 Figure G7. Species concentrations calculated as a function of temperature at a constant XEn=0.5 for the calibrated orthopyroxene speciation model 196 Figure G8. Calculated t o t a l free energy of mixing for the orthopyroxene speciation model as a function of X^„ 1 97 ix L i s t of Plates Plate 1. Low magnification bright f i e l d images of the synthetic orthoamphiboles 159 Plate 2. High magnification images and electron d i f f r a c t i o n patterns for specimens in ( O k l ) or ientat ion 163 Plate 3. Electron d i f f r a c t i o n patterns and one high magnification image for specimens in ( h O l ) orientation 165 x Acknowledgements I g r a t e f u l l y thank a l l of those who provided help and support along the way. Dr. H.J. Greenwood provided u n f a i l i n g academic and f i n a n c i a l support throughout the study. Dr. Martin Engi contributed many f r u i t f u l discussions and his personal cooperation with the database c a l c u l a t i o n s . Dr.'s T.H. Brown, E.P. Meagher and R.G. Berman and Derry McPhail also contributed to f r u i t f u l discussions. Dr.'s Greenwood, Engi and Brown have a l l reviewed preliminary portions of t h i s document. Dr.'s Scudder and Calvert each generously provided access to needed a n a l y t i c a l equipment. Invaluable technical support was provided by Ed Montgomery (photography), Bryon Cranston (probe mounts), John Knight (microprobe), Mary Mager (TEM), Laurie Frederick (TEM) and Lyle Hammerstrom (hydrothermal l a b ) . xi I. Ion-Exchange Equilibrium with Mg-Fe Olivine and Modelling of the Aqueous Solution INTRODUCTION Experimental and theoretical investigation of the Fe-Mg o l i v i n e s o l i d solution has recieved considerable attention in the l i t e r a t u r e . Most of the experimental contributions are Fe-Mg ion-exchange experiments studying the equilibrium of o l i v i n e with orthopyroxene (Nafziger and Muan, 1967; Kitayama and Katsura, 1968; Medaris, 1969; Williams, 1971; Matsui and Nishizawa, 1974), or garnet (Kawasaki and Matsui, 1977; O'Neill and Wood, 1979; Kawasaki and Matsui, 1983), or spinel (Engi, 1978, 1983), or ilmenite (Andersen and Lindsley, 1979, 1981), or Fe-Mg chloride aqueous solutions (Schulien, Friedrichsen and Hellner, 1970). Contributions using calorimetry include Sahama and Torgeson(1949), Wood and Kleppa(1981), and Thierry et a l ( l 9 8 l ) . Additional e f f o r t s to analyze (or reanalyze) portions of the experimental data include work by Wi11iams(1972), Saxena(1972), Obata, Banno and Mori(l974), Engi(l980a) and Sack(1980). This chapter is aimed at making two contributions. 1) To extend an o l i v i n e solution model with confidence down to temperatures where o l i v i n e is important as a metamorphic mineral. 2) To c r i t i c a l l y evaluate the u t i l i t y of aqueous chlorides, 1 2 p a r t i c u l a r l y Fe-Mg chlorides, for characterizing s o l i d solutions through ion-exchange experiments. Of the above exchange equilibrium experimental studies, only Schulien et al(l970) and Andersen and Lindsley(1979) provide data below 800°C which span the Fe-Mg composition range. The Fe-Mg exchange equilibrium experiments reported here were performed over a range of conditions from 450 to 800°C and 1 to 4 kbar using aqueous Fe-Mg chloride solutions as the second phase. Although Schulien et al(l970) performed similar experiments under similar conditions, the size of their compositional error brackets r e s t r i c t s their study to qu a l i t a t i v e characterization of the o l i v i n e s o l i d s o l u t i o n . Aqueous chlorides have been in use as ion-exchange media for over 20 years. Some workers have simply used aqueous chlorides as a flux to speed up reaction and r e c r y s t a l l i z a t i o n rates of s o l i d phases (e.g. Gunter, 1974; Medaris, 1969). Ion-exchange experiments which consider aqueous chlorides as an equilibrium phase have been performed with nepheline (Debron et a l , 1961), a l k a l i - f e l d s p a r ( O r v i l l e , 1963), o l i v i n e (Schulien et a l , 1970), plagioclase ( O r v i l l e , 1972), scapolite (Wellman, 1970; E l l i s , 1978), Ca-garnet, epidote (Perchuk and Aranovich, 1979) and b i o t i t e (Schulien, 1980). The attractions of aqueous chlorides as an exchange medium include: faster reaction rates, an assumed lack of compositional inhomogeneity in the aqueous s o l u t i o n , ease of 3 phase separation for independent chemical a n a l y s i s , and the common assumption that the mixure of chlorides in aqueous solution could be treated as an ' i d e a l ' s o l u t i o n . Engi(1980b) has already pointed out the f a l l a c y of this l a s t assumption for Fe-Mg chloride solutions. To help evaluate the role of the chloride solution in the study presented here, additional experiments were conducted at constant o l i v i n e s t a r t i n g composition while varying the t o t a l concentration of chlor i d e s . Using this data along with published studies of aqueous e l e c t r o l y t e properties, a working model i s established for the behavior of the Fe-Mg chloride solution within the range of conditions spanned by the ion exchange experiments. EXPERIMENTAL TECHNIQUES STARTING MATERIALS: Synthetic o l i v i n e s were made from reagent grade oxides at composition intervals of 0.1 X^o (mole fr a c t i o n of the f o r s t e r i t e endmember). The iron bearing o l i v i n e s were synthesized using Method 2 of Turnock, Lindsley and Grover(1973) . Oxygen-balanced mixes made from F e ° , Fe203 , MgO and Si02 ( c r i s t o b a l i t e ) were loaded into p u r e - s i l i c a 4 glass tubes isolated from the glass by Ag7 0Pd3 0 f o i l . The tubes were evacuated, sealed, and heated at 1050°C for 3 to 6 days, depending on mix composition. The products of the f i r s t heating were ground, reloaded and reheated for a similar length of time. In general, the more Fe-rich compositions reacted more quickly and grew to a larger grain s i z e . The Mg end-member mix was heated in a i r at 1400°C for 24 hours, ground, and heated for another 24 hours. A l l synthesis products were examined both o p t i c a l l y and by XRD and found to contain 99% or more o l i v i n e . Grain sizes ranged from <2um for the magnesian compositions to 1-5/im for the Fe-rich compositions. Endmember chloride solutions at 2 molal concentration were prepared from reagent grade MgCl2'6H20 and FeCl2*4H20. Intermediate composition solutions were prepared by mixing the end-members. The Fe and Mg concentrations in each of these solutions was checked by standard flame atomic absorption. In some cases, solutions of intermediate composition were created in the run capsule by pipetting small aliquots of the end-member solutions into the capsule and c a r e f u l l y weighing each a l i q u o t . Run solutions at concentrations less than 2m were created the same way, using d i s t i l l e d water as one a l i q u o t . Densities determined by weighing known volumes of the end-member solutions allowed conversion of weights to volumes and conversion of molality to molarity when needed. 5 ION EXCHANGE EXPERIMENTS: Weighed amounts of o l i v i n e and chloride solution were sealed into noble metal capsules. A t y p i c a l run capsule contained 40 to 70mg of o l i v i n e and s o l i d - t o - f l u i d weight ratios were t y p i c a l l y 1 to 2. I n i t i a l compositions were chosen to produce opposing brackets on the equilibrium. Gold capsules were used above 600°C, both gold and Ag6opcUo capsules were used at 600°C, and both Ag60Pdi,o capsules and thin-walled (.1mm) gold capsules were used below 600°C. A l l runs were made in 3.2x30.5cm cold-seal pressure vessels; either S t e l l i t e 25 or Rene 41. A quick-quench configuration (5cm f i l l e r rod, unextended bomb) was used above 600°C so that, when quenching, the capsule could be dropped close to the cool end of the bomb (see also Wellman, 1970). Full-length steel f i l l e r rods were used at and below 600°C. In a l l cases, the bomb was cooled with a stream of compressed a i r with water aspirated into the stream. The results of a few quick-quench runs at 600°C could not be distinguished from the rest of the 600°C data set. Run temperature was measured with a calibrated chromel-alumel thermocouple inserted into an external well in each bomb. The temperature difference between th i s external well and the run capsule position was calibrated once for each bomb using a working standard thermocouple which had been cali b r a t e d against a 'lab standard' thermocouple. This lab standard thermocouple had been calibrated against NBS melting point standards. The bomb c a l i b r a t i o n was performed 6 at 1atm for f u l l - l e n g t h f i l l e r rod configurations and at 1 and 2 kbar for quick-quench configurations. The combination of c a l i b r a t i o n and time-variation temperature errors i s estimated to be no more than ±5°C. The pressure medium was methane for the 1 and 2 kbar runs. The hydrogen pressure established by the graphite-methane equilibrium prevented oxidation of the capsule contents for runs at and above 600°C. Below 600°C , a higher hydrogen pressure was needed to keep f_ in the capsule below that of the fayalite-magnetite-quartz buffer. To accomplish t h i s , H2 was introduced into the bomb before pressurizing with methane, and graphite was not introduced. The amount of H2 added was designed to result in a H2 p a r t i a l pressure between values calculated for the fayalite-magnetite-quartz-H20 equilibrium and .the magnetite-wiistite-H2 equilibrium. At T>600°C, the amount of graphite which precipitated from pure CH„ while reaching the CH„ = C + H2 equilibrium was usually s u f f i c i e n t to prevent 'drop' quenching. Hydrogen was added to these runs to minimize t h i s p r e c i p i t a t i o n . The runs at 4kbar were pressurized with water. For these runs a button of graphite introduced along with the run capsule was found to prevent oxidation at 600°C. The goal of these f0 control techniques was to keep the experimental f~ s l i g h t l y below FMQ rather than buffering fn to a calculable value. Pressure on the u2 methane l i n e was measured with an Ashcroft gauge calibrated against a factory calibrated 2000bar Heise gauge. At 4kbar, pressure was measured with a 7000bar Heise gauge. Stated 7 pressures are considered accurate to within 60 bars. Following each experiment the capsule was cleaned, weighed, punctured with a needle at both ends and placed in an argon-flushed 1ml centrifuge v i a l (Pierce ' R e a c t i - V i a l ' ) . The v i a l was sealed and centrifuged. T y p i c a l l y 50 to 70% of the run f l u i d was extracted and any solids extracted with the f l u i d were simultaneously centrifuged out. For a few runs, quench pH was measured d i r e c t l y on the centrifuged run f l u i d with a micro-combination electrode. That portion of the extracted f l u i d which could be drawn off uncontaminated by solids was diluted with s l i g h t l y a c i d i f i e d (0.03m HN03) d i s t i l l e d water in preparation for chemical an a l y s i s . Whenever s u f f i c i e n t f l u i d could not be extracted by centr i f u g i n g , the capsule was cut open and the contents washed into the centrifuge v i a l with d i s t i l l e d water. The v i a l was sealed, agitated and centrifuged and the supernatant l i q u i d was drawn off and dilu t e d with a c i d i f i e d water . The s o l i d products of each experiment were washed with d i s t i l l e d H20, centrifuged, washed with alcohol, centrifuged and dr i e d . FINAL COMPOSITIONS: The concentrations of Fe and Mg in the diluted product solutions were measured with standard acetylene-flame atomic-absorption techniques. Total CI in a representative portion of these product solutions was measured with a 8 Buchler-Cotlove chloridometer. Since the volume of aqueous solution could not always be accurately determined, only concentration ratios and mole fractions were used in subsequent numerical analysis of aqueous e q u i l i b r i a and ion-exchange e q u i l i b r i a . A l l s o l i d products were examined o p t i c a l l y and many were checked with XRD. In addition to o l i v i n e , the s o l i d products of a majority of the ion-exchange experiments included an Mg-Fe s i l i c a t e more s i l i c e o u s than o l i v i n e . This additional phase was either quartz, t a l c , orthopyroxene or orthoamphibole and i t s modal amount was generally less than 2%, but occasionally up to 5%. The identity of the accessory phase at each pressure, temperature and bulk composition provides information about the s t a b i l i t y of the accessory phases from a synthesis-experiment point of view. The presence of these s i l i c e o u s accessory phases was attributed to incongruent dissolution of the o l i v i n e into the aqueous solution at P and T. Since the concentration of aqueous CI is constant, non-chloride species of Mg and/or Fe must have been present at P and T. Traces of a green, amorphous substance found in many of the experimental run products may be a precipitate formed from these non-chloride species upon quenching. F i n a l o l i v i n e compositions were established by one or more of 4 methods. Three of these are electron microprobe techniques and the fourth is a mass-balance c a l c u l a t i o n . Olivine f i n a l compositions calculated by mass-balance were 9 considered to be more than just approximations for two reasons: (1) Individual weights of the i n i t i a l phases were known to ±0.2mg out of 30 to 60mg. (2) Due to large molar ratios of (Mg,Fe)Si0.502 to (MgrFe)Cl2 ( t y p i c a l l y 10 to 20), propagation of f l u i d analysis errors through the mass-balance results in standard errors similar to those t y p i c a l of the microprobe analyses. The possible weaknesses of the mass-balance calculations are zoning of the ol i v i n e grains and the unaccounted-for effect of minor product phases. The three microprobe techniques used were standard analysis, p a r t i c l e a n a l y s i s , and crystal-face analysis. For standard a n a l y s i s , product o l i v i n e grains were hot-pressed into Buehler 'Transoptic' p l a s t i c and polished with diamond abrasives. Synthetic end-member o l i v i n e grains (50 to 150Mm), i d e n t i c a l l y mounted, were used as standards and the correction procedures of Bence and Albee(1968) and Albee and Ray(l970) were used. The operating conditions were l5kV with 15nA specimen current. Mg, Fe and Si were analyzed simultaneously employing 20 second counting times. For each sample, 6 to 10 analyses were averaged. A portion of the analyses were done on an automated ARL-EMX at the University of Washington, Seattle, and the remainder were done at the University of B r i t i s h Columbia on an ARL-SEMQ. Standard analysis was judged inadequate for a majority of the samples for 2 reasons: (1) The o l i v i n e grain size in some samples was too small to contain the beam and i t s excitation volume. 10 (2) Compositional zoning was inferred to be present in many samples. For 15 to 2bixm grains (a very common size range) only core analyses would produce acceptable t o t a l s and stoichiometry. Fine (5fim) scale compositional zoning was inferred to be present in many of these grains by comparing microprobe and mass-balance compositions. If the two compositions were s i g n i f i c a n t l y d i f f e r e n t , the probe composition (X^) was, with few exceptions, between the mass-balance and the i n i t i a l X^Q, or, in extreme cases, id e n t i c a l to the i n i t i a l X ^. For grains larger than 25*xm, analyses were taken as close as possible to grain edges, but, once again, edge zoning on a 5#m scale could not be measured d i r e c t l y . To eliminate minimum grain size and fine-scale zoning problems, many samples were analyzed with p a r t i c l e analysis techniques. The o l i v i n e grains were dispersed on polished graphite stubs and carbon coated. While operating at I 5 k v and 35nA on the ARL-SEMQ, the beam was rastered over a lOum square. Secondary electron imaging made i t possible to select grains en t i r e l y containable within the lOjum square for a n a l y s i s . Mg, Fe and Si were analyzed simultaneously employing 40 second counting times. A f i r s t approximation of p a r t i c l e formula composition was established using the same standardization and correction procedures described above for standard analysis. An empirical correction curve was established by using the same procedures to analyze a l l of 11 the synthetic o l i v i n e s used as start i n g materials. Each p a r t i c l e analysis reported i s an average of 10 to 15 individual analyses. Some of the higher temperature run products did not contain o l i v i n e grains smaller than lO/nm and could not be analyzed using the same p a r t i c l e analysis procedures. Edge compositions were measured for several of these large-grain samples using standard analysis techniques on p a r t i c l e analysis mounts. Most of the product o l i v i n e s were quite euhedral. As a r e s u l t , many of the grains dispersed for p a r t i c l e analysis l i e f l a t on their largest c r y s t a l face: (010). The upper (010) face is then both f l a t and hor i z o n t a l . Standard analysis of (010) faces larger than 15um across produced acceptable t o t a l s and formula. Comparison of standard microprobe analyses with the p a r t i c l e and c r y s t a l face analyses tends to confirm the existence of the fine scale zoning which was o r i g i n a l l y only inferred to be present. The points plotted on figure 1.1 i l l u s t r a t e the difference between p a r t i c l e and standard analyses (X^o(particle)-X^o(standard)) for cases in which both techniques had been applied. The triangular symbols point in the di r e c t i o n of zoning displacement predicted by the dir e c t i o n of approach toward equilibrium in the ion-exchange experiment. 12 0.10 o c D -M 00 _0) o 0.05-0.00 O -0.05 QL - 0 . X fo Figure 1.1 Comparison of standard and p a r t i c l e analyses for cases in which both techniques were applied to samples of the same product o l i v i n e s . The triangular symbols point in the d i r e c t i o n of edge-zoning displacement which would be predicted considering the d i r e c t i o n of approach toward ion-exchange equilibrium for each experiment. 1 3 DATA ANALYSIS Run conditions and compositions for the c r i t i c a l runs are l i s t e d in table 1.1. A plot of Xj^gd v s XfD (figure 1.2) i l l u s t r a t e s the magnitude of compositional changes and compositional precision for the runs at 2kb, 600°C, 2m c h l o r i d e . To monitor the thermodynamic behavior of the system, a more useful visual representation i s a plot of lnKD against X^o at constant T and P, where KD is the d i s t r i b u t i o n c o e f f i c i e n t of the o v e r a l l exchange reaction: Mg(olivine) + Fe(aq) = Fe(olivine) + Mg(aq) (1) KD = X f a (2) XF e C l2 Xf o Figure 1.3 i l l u s t r a t e s the trends on such a plot for hypothetical cases in which the aqueous solution i s thermodynamically ' i d e a l ' . Figure 1.8 shows lnKD vs X^ plots of the 2m data along with theoretical models which are explained below. The apparent influence of t o t a l chloride molality, mT, on the ion-exchange equilibrium i s i l l u s t r a t e d in figure 1.6. The general c h a r a c t e r i s t i c s of the data that influenced the nature of the physical and thermodynamic models used in analyzing the data are: the approximately linear trend of Table 1.1. Ion-exchange run data. - - -INITIAL- - - MINOR - - - - - - - - - - FINAL - - - - - - - - - - -PRODUCT RUN* T('C) P(kb) HOURS X, X,. mT PHASES X,. Cl/Mg+Fe X, HOW 1 nKn 1o fo Mg T Mg ro D 142 450 996 0 400 0 000 2 0 TA2 0 296 1 .94 0 338 P -0 13 0 10 143 450 1 996 0 400 0 700 1 0 0 334 1 .87 0 455 P -0 44 0 07 145 450 1 1000 0 104 0 500 2 0 0 251 1 .85 0 163 P 0 61 0 07 146 450 1 100O 0 710 0 700 2 0 TA 0 504 1 .87 0 728 P -0 90 0 05 147 450 1 1000 1 000 0 700 2 0 TA 0 759 1 .87 0 984 P -2 91 0 64 163 450 1 840 0 104 0 000 2 0 0+OA 0 094 1 85 0 074 P 0 33 0 17 164 450 1 840 0 400 0 500 0 2 O+TA? 0 374 1 67 0 4 19 P -0 12 0 06 165 450 2 842 0 400 0 100 2 0 TA 0 450 1 67 0 334 P 0 55 0 06 166 450 2 842 0 400 0 100 O 5 TA 0 506 1 62 0 347 P 0 72 0 07 167 450 2 842 0 400 0 500 0 2 TA 0 588 - - 0 388 P 0 88 0 07 1 16 600 1 510 0 496 0 100 2 0 TA 0 152 - - 0 492 M - 1 62 0 05 1 17 600 1 ' 528 0 496 0 500 0 2 TA 0 146 -- 0 504 M - 1 72 0 05 121 600 1 435 0 496 0 000 0 2 TA? 0 120 2 1 1 0 478 P - 1 84 0 06 122 600 1 436 0 496 0 500 2 0 OP 0 205 1 90 0 529 P - 1 4 1 0 09 124 600 1 436 0 800 0 500 2 0 TA 0 4 1 1 1 81 0 807 P - 1 73 0 07 135 600 1 650 0 496 0 500 1 0 OP 0 156 2 02 0 582 P - 1 95 0 10 136 600 1 650 0 496 0 000 0 5 0 106 2 07 0 472 P - 1 95 0 08 199 600 1 627 0 104 0 300 2 0 OA 0 040 1 94 0 123 P - 1 15 0 08 200 600 1 627 0 300 0 300 2 0 OA 0 095 -- 0 327 P -1 47 0 1 1 25 600 2 240 0 104 0 100 2 0 • A 0 070 -- 0 101 S -o 34 0 06 26 600 2 240 0 300 0 200 2 0 OA 0 157 -- 0. 299 P -0 76 0 1 1 27 600 2 240 0 300 0 000 2 0 OA 0 138 -- 0 270 P -o 77 0 10 Table 1.1. (continued) - - -INITIAL- - - MINOR - - - - - - - - - - FINAL ?UN/C T('C) P(kb) HOURS f o Mg m. T PRODUCT PHASES Mg Cl/Mg+Fe Xf o HOW1 lnK D 1<J 37 600 2 338 0 .600 0 . 300 2 .0 TA 0 . 265 -- 0 .607 P - 1 . 39 0.07 38 600 2 338 0 .710 0 . 100 2 .0 TA 0 .275 - - 0 .679 P -1 .65 0.08 39 600 2 697 0 . 800 0 . 200 2 .0 TA 0 . 359 -- 0 .770 P - 1 . 72 0.06 40 600 2 697 0 . BOO 0 .500 2 .0 TA 0 . 443 -- 0 .792 P -1 .50 0.08 4 1 600 2 697 0 .900 0 .400 2 .0 TA 0 .524 - - 0 .882 P -1 .85 0.08 42 600 2 697 0 900 0 . 700 2 .0 TA O .617 -- 0 .909 P -1 .76 0. 10 43 600 2 360 0 . 496 0 .OOO 2 .0 OA 0 . 200 0 .465 P -1.18 0.06 64 600 2 1212 o . 800 0 .900 2 .0 TA 0 .685 1 . 82 0 . 942 M - 1 . 95 0.19 66 600 2 1436 0 .496 0. .300 2 .0 OA+TA 0 .219 1 .93 0 .500 M -1.21 0.05 67 600 2 1436 0. . 496 0. OOO 0 . 2 OA + TA 0. . 154 2 .09 0 .501 P - 1 .64 0.05 68 600 2 1436 o 496 0. .500 0 . 2 OA + TA 0. . 166 2.09 0 . 503 S -1 .56 0.06 1 19 600 2 435 0 496 0. 500 0 . 5 0. 184 -- 0 .533 P -1 .56 0.06 133 600 2. 758 0 496 0. 000 1 .0 0. 189 1 . 94 0 .463 P - 1 . 24 0.06 134 600 2 758 0. 496 0. 000 0 .5 0. 165 2 .05 0 482 M - 1 . 48 0.05 101 600 4 382 o. 496 0. 000 2 .0 OA+TA 0. 269 0. 474 P -0.83 0.08 102 600 4 382 0. 496 0. 000 0 . 2 TA 0. 352 -- 0. 503 P -0.56 0.06 103 600 4 382 o. 496 O. 500 0 . 2 TA 0. 387 -- 0. 472 P -0. 28 0.05 128 600 4 385 o. 496 0. 500 2 .0 TA 0. 4 10 1 . 79 0. 519 P -0. 37 0. 10 129 600 4 385 0. 496 0. 100 1 .0 TA 0. 369 1 .85 0. 465 P -0.33 0.07 130 600 4 385 0. 496 0. 100 0 .5 0. 376 - - 0. 469 P -0. 32 0.06 174 600 4 601 0. 900 0. 300 2 .0 TA 0. 577 1 .67 0. 855 P - 1 . 40 0.09 197 600 4 530 0. 104 0. 000 2 . .0 0 0. 060 1 .93 0. 078 P -0.22 0. 10 225 600 4 579 0. 104 0. 300 2 .0 OA 0. 126 1 . 93 0. 130 P 0.03 0. 13 Table I.1 (cont i nued) - - -INITIAL- - - MINOR - - - - - - - - - - FINAL RUN* TC C) P(kb) HOURS X. f o Mg m T PRODUCT PHASES Mg Cl/Mg+Fe f o HOW1 lnKD 1<J 226 600 4 579 0 . 300 0. OOO 2 .0 OA 0 . 189 - - 0 .270 P -0.40 0.08 227 600 4 579 0 . 800 0. . 900 2 .0 TA 0 . 598 0 .820 P -1 .05 0.09 69 725 2 1 106 0 . 104 0. .000 2 .0 0 0 .023 1 .99 0 . 102 M -1.51 0.07 70 725 2 1 106 0 . 104 O. 100 2 .0 0 0 .024 2 .03 0 . 107 S - 1 . 52 0.05 71 725 2 1 106 0. . 400 O 300 2 .0 OP 0 .089 1.91 0 . 423 S - 1 . 95 0.05 72 725 2 1 105 o 800 0. 500 2 .0 OP 0 . 308 1 .88 0 .811 s -2 . 20 0.05 21 1 725 2 351 o 800 0. 100 2 .0 OP 0 . 287 1 .99 0. .780 p -2.11 0.07 2 12 725 2 351 0 .600 0. 300 2 .0 OP 0 . 175 -- 0. .623 p -1 .99 0.05 2 13 725 2 351 0. 400 0. 000 2 .0 OP 0 .088 -- 0. 392 p -1.83 0.05 75 800 2 1 101 0 104 0. 100 2 .0 0 .031 - ' - 0. . 105 S - 1 . 23 0.06 169 800 2 494 o. 800 0. 700 2 .0 OP 0 .404 1 . 73 0. 877 F -2.29 0.07 170 800 2 494 o. 800 0. 100 2 .0 OP 0 329 1 . 38 0. 825 F -2 . 20 0.07 202 800 2 256 0 104 0. 000 2 .0 0 0 .015 1 . 59 0. 113 P -2 .06 0.05 203 800 2 256 0. 400 0. 300 2 .0 OP 0. .083 1 .84 0. 420 S -2.01 0.08 204 800 2 256 o. 7 10 0. 500 2 .0 OP 0. 244 - - o. 745 P -2.14 0.08 Method of f i n a l X^ . determination: M=mass balance, S=standard microprobe, P=particle analysis, F=crystal face a n a l y s i s . OA=orthoamphibole, OP=orthopyroxene, TA=talc, and Q=quartz. 1.0-17 0.8-LU Q 0.6 CC o _l X o g> 0.4-2kb 600°C 2m CHLORIDE 0.2-— i — 0.4 1 1 1 i r 0.2 0.6 X M g OLIVINE 0.8 1.0 Figure 1.2 Compositional changes measured for ion-exchange experiments at 600°C, 2kb. The s o l i d l i n e connects i n i t i a l and f i n a l compositions. F i n a l compositions are surrounded by 1a error boxes. 18 IDEAL SOLID SOLUTION ^ ^ ^ ^ ^ % s. v> \ IDEAL AQUEOUS SOLUTION X fo Figure 1.3 Theoretical trends of lnK_ vs Xf given that the 3 D to 3 aqueous f l u i d behaves as a thermodynamically ideal solution of the chloride endmembers. Non-ideal s o l i d solution examples assume a Margules formulation. 19 lnKD vs X^o at each temperature, the decrease in lnKD with mT at 600°C, and the possible increase in lnK^ with decreasing mT at 450°C (the lack of opposing pairs of half-brackets at 450°C leaves t h i s trend poorly constrained). Note also the scatter of Cl/(Mg+Fe) data around some value less than 2.0. The data analysis attempts to answer the following quest ions: Can the application of previously established knowledge of aqueous e l e c t r o l y t e s account for those features of the data dependent only on the properties of the aqueous solution? How do uncertainties in thi s interpretation of the aqueous solution properties affect subsequent analysis of the ol i v i n e s o l i d solution? Is there a thermodynamic s o l i d solution model that i s consistent with the present data and with a l l previously published experimental studies of Mg-Fe o l i v i n e solution behavior? THE AQUEOUS SOLUTION'. In the past, most theoretical interpretations of chloride ion-exchange data have treated the aqueous solution as thermodynamically ' i d e a l ' (or i t s equivalent). Orvilie(1963, 1972) concluded, on the basis of a few 20 experiments over a range of chloride concentrations, that ion-exchange equilibrium of aqueous chlorides with feldspars was independent of t o t a l chloride concentration. Based on this conclusion, he treated the aqueous solution as ideal when interpreting his experiments. Perchuk and Aranovich(1979) based their assumption of i d e a l i t y in A l C l3- F e C l3 mixtures on experiments with KCl-NaCl solutions (Perchuk and Andrianova, 1968). Schulien(1980) based his assumption of i d e a l i t y in MgCl2-FeCl2 mixures on a qu a l i t a t i v e conclusion that the neutral MgCl2 species mixes id e a l l y with H20 (Frantz and Popp, 1979) and did not attempt to test t h i s assumption experimentally. In contrast, Saxena(l972) analyzed the ion-exchange data of Schulien et al(l970) by modelling the bulk properties of the Mg-Fe chloride solution with a Margules-type excess function. In doing so he chose to ignore the identity of the actual Fe and Mg species in the aqueous s o l u t i o n . Thompson and Waldbaum(1968), in analyzing the data of Orville(1963), considered the p o s s i b i l i t y that KC1 and NaCl are p a r t i a l l y dissociated to Na+, K+ and CI". However they only considered the case in which KC1 and NaCl are dissociated to the same extent and proceeded to show that t h i s case was indistinguishable from the 'ideal solution' assumption when analyzing the ion-exchange equilibrium. Engi(l980) demonstrated the consequences of contrasting dissociation-equilibrium constants in a binary aqueous chloride solution by applying q u a l i t a t i v e equilibrium 21 constant data for MgCl2 = Mg+2 + 2C1" (Frantz and Popp, 1979) and FeCl2 = Fe+ 2 + 2C1" (Boctor et a l , 1980) to the o l i v i n e exchange equilibrium data of Schulien et a l ( l 9 7 0 ) . In general, aqueous e l e c t r o l y t e s are e s s e n t i a l l y e n t i r e l y dissociated into charged species at STP and become increasingly associated with increasing T and decreasing P. Although a large amount of quantitative data has been published for many aqueous e l e c t r o l y t e compounds, only a small portion of the measurements were made at pressures and temperatures above.the c r i t i c a l point of H20 (see Helgeson et a l ( l 9 8 l ) for compilation, c r i t i q u e and a n a l y s i s ) . More s p e c i f i c a l l y , the data available on the behavior of MgCl2 in s u p e r c r i t i c a l H20 are incomplete and s u p e r c r i t i c a l data for FeCl2 solutions are scant. Figure 1.4 i l l u s t r a t e s the available d i s s o c i a t i o n constant data for chloride compounds at P-T conditions pertinent to t h i s study. These di s s o c i a t i o n constants have been derived from e l e c t r i c a l conductivity measurements by the authors l i s t e d in table 1.2. The curves in figure 1.4 were generated with the empirical function used by Frantz and Marshall(1982): logKMd i s s = a + b/T + clogpH20 (3) where KM i s an equilibrium constant on the molarity concentration s c a l e , T i s in kelvins, pH20 i s the density of pure H20 at P and T of i n t e r e s t , and a, b and c are empirical f i t parameters. Conversion to the molality 22 400 450 500 550 600 650 700 750 800 Temperature (°C) Figure 1.4 Common logarithm of aqueous chloride d i s s o c i a t i o n constants at 2kb. See text for explanations and table 2 for references. 23 Table 1.2. F i t parameters for equation (3) for several aqueous ch l o r i d e s . See text for d e t a i l s . a b c DATA ' SOURCE REGRESSION TO EQUATION (3) NaCl -1 .43 1470 10.2 1 5 KC1 -2.68 590 3.26 2 5 L i C l -2.61 970 3.65 3 5 BaCl2 K, -3.97 1 530 6. 1 3 2 5 K2 -6.24 2580 7.39 2 5 CaCl2 K, -3.21 2407 10.6 4 4 K2 -5.05 3112 16.5 4 4 MgCl2 K 1 (-3.21 ) (2407) (10.6 ) 4 4 K2 -4.80 3415 19.2 4 4 1: Quist and Marshall(1968) 4: Frantz and Marshall(1982) 2: Ritzert and Franck(l968) 5: This study 3: Mangold and Franck(!969) concentration scale (which i s used in figure 1.4 and throughout the remainder of this paper) was done with the approximation: l o9Kd i s s = l o g K Md i s s " l o9 PH2° which i s reasonably accurate for d i l u t e solutions. Portions of some of the curves in figure 1.3 extend beyond the data from which they were derived. Table 1.2 l i s t s the f i t parameters for equation (3) for each compound along with the appropriate references. Note that, for several pairs of c h l o r i d e s , the dissociation constants may be i d e n t i c a l at 24 one temperature and an order of magnitude apart at a temperature 200°C (or less) away. For the d i c h l o r i d e s , two d i s s o c i a t i o n constants are calculated; one for each of two step-wise di s s o c i a t i o n reactions: MC12 = MC1+ + CI" and MC1 + = M+2 + CI". Experimental d i f f i c u l t i e s attributed to hydrolytic p r e c i p i t a t i o n of MgO or Mg(OH)2 prevented Frantz and Marshall(1982) from d i r e c t l y measuring the f i r s t d i s s o c i a t i o n constant of MgCl2. They inferred from what data they did gather that K,MgCl2 could be treated as i d e n t i c a l to K,CaCl2. Only q u a l i t a t i v e information i s available for the d i s s o c i a t i o n e q u i l i b r i a of aqueous F e C l2. S o l u b i l i t y studies of magnetite (Chou and Eugster, 1977) and hematite (Boctor et a l , 1980) in s u p e r c r i t i c a l Fe-chloride solutions were interpreted by their authors to indicate that associated FeCl2 i s the dominant aqueous species from 400 to 650°C at 2kb and from 400 to 600°C at 1kb. In l i g h t of the dearth of quantitative information for FeCl2 speciation, a s i m p l i f i e d model of the Mg-Fe chloride aqueous solution has been adopted here in an attempt to account for the dependence of lnK^ on t o t a l chloride concentration. Here are the features of that model, referred to as the f i r s t - d i s s o c i a t i o n model in following discussions: A) The dominant ion-exchange equilibrium was assumed to be: 25 MgSi0.502 + FeCl2 = F e S i0.502 + MgCl2 (5) K = ( l'Xfo) mMqCl2('yfa^MgCl2) ( f i )  E Xf o mF e C l2( 7f o7F e C l2) A c t i v i t i e s of the aqueous species were assumed to be influenced only by interaction with H20. Mixing of the aqueous species with each other was assumed to be i d e a l . B) Only the f i r s t d i s s o c i a t i o n reactions for the chlorides were considered. Figure 1.4 i l l u s t r a t e s that t h i s s i m p l i f i c a t i o n may be j u s t i f i e d since, over the temperature range of interest here, K2MgCl2 is more than 1 log unit below fc^MgClz. MgCl2 = MgCl+ + CI" (7) K = mMgCl+mCl-( 7MgCl+7Cl-) ( 8 ) M g m (<v ) mMgCl2 WM g C l2; FeCl2 = FeCl+ + C l " (9) 26 K = mF e C l +mC l -(7F ec i *7C l -} ( 1 0) mF e C l2 ( 7F e C l2) C) MgCl2, F e C l2, MgCl+, F e C l+, and CI" were the only aqueous species considered. In other words, a l l possible reactions of these species with the solvent, H20, were ignored. Therefore: K _ ° "Xf o) ( mMqd2 + mM g dJ ( n )  Xf o ( mF e C l2 + mF e C l+ ) Although Helgeson et a l ( l 9 8 l ) provide an extended Debye-Hiickel a c t i v i t y c o e f f i c i e n t equation applicable to any aqueous species over a wide range of P, T and concentration, once again the lack of appropriate experimental data to quantify the f i t parameters precludes i t s direct application to the species considered here. D) A c t i v i t y c o e f f i c i e n t s of a l l neutral species were assumed to be 1.0, and a l l singly charged species were assumed to have i d e n t i c a l a c t i v i t y c o e f f i c i e n t s . These a c t i v i t y c o e f f i c i e n t s were calculated with an unextended Debye-Hiickel expression - Z2A ( I ) ° -5 l o g7. = (12) 1 1+aB(l)0'5 where Z i s the ionic charge, I i s the true ionic strength, A and B are the Debye-Hiickel c o e f f i c i e n t s and a i s the 27 ion-size parameter. A value of 4.0 was judged appropriate for a based upon values tabulated for MgCl2, Fe C l2 and NaCl (Helgeson et a l , 1981). A and B were taken from Helgeson and Kirkham(1974) up to 600°C and were extended to 800°C with equations (2) and (3) of Helgeson and Kirkham(1974) along with H20 d i e l e c t r i c constants provided by Quist and Marshall(1965). The standard states i m p l i c i t in the above formulation are: the pure s o l i d phase at P and T, and a hypothetical ideal 1-molal aqueous solution at P and T. The mass-balance constraints on the model are: mT = V j C I , + mMgCl* + mF e C l2 + mF e C l+ ( 1 3 where mT i s the t o t a l molality of Mg+Fe in aqueous solution and: mC l " = mMgCl+ + mF e C l+ ( 1 4 ) From (14) i t follows that I = mcl_ (15) Equations (6), (8), (10), (13) and (14) can be combined and manipulated to produce a quadratic in the molality of one species which can, in turn, be solved for a r e a l , positive root. Using a substitution derived from (6): 28 Q = " V1* = 7 f° X f° KF (16) mF e C l2 7f a( 1-Xf o} and solving for mMg d + results i n : 0 = S^ (Q + + b ) mM9Cl+ + b mMgCl* - mT ( 1 7 ) y Mg Mg where K QK b = 1 + (18) Mg The d i s t r i b u t i o n of aqueous species predicted by this model was calculated in an i t e r a t i v e procedure which solved (17), calculated (combining (8), (10), (14), and (16)), calculated 7C^- (with (12) and (15)) and tested for satisfactory convergence on 7Q±-' KMg was taken from Frantz and Marshall(1982), and KF g was modelled with equation (3), requiring 3 f i t parameters. Figure 1.5 shows the influence of e l e c t r o l y t e d i s s o c i a t i o n on the o l i v i n e exchange KD as predicted by the f i r s t - d i s s o c i a t i o n model. The i l l u s t r a t i o n is for the hypothetical case in which the o l i v i n e s o l i d solution i s i d e a l , lnK^, = -1.0, logKM g = -2.0, 600°C, 2kb and where ALK = l o g KMg " l o g KF e a n d Kav = ( l o g KM g+ l o g KF e} / 2' I f A L K = 0*0' then lnK^ i s i d e n t i c a l to InK,,. If ALK i s d i f f e r e n t from 0.0 then lnKD - lnK^ has the same sign as ALK and i t s absolute value increases as |ALK| increases, as K increases, and as 3 V mm decreases. The influence of X, on l n K „ - lnK„ is quite T fo D E ^ small except possibly near the l i m i t s of 0 -- 1 -_E - 2 -- 3 -- 4 I I I I !nK£=- 1.0 l ° g K M g = - 2 - 0 m T logKpe ALK Kov 0.2 -3 .0 +1.0 -2.50 2.0 -3 .0 + 1.0 — - 2 . 5 0 • 2.0 -2 .0 0.0 -2.00 2.0 -1.5 -0 .5 -1.75 2.0 -1.0 -1.0 -1.50 600°C 2kb Ideal Olivine I I I I 0.0 0.2 0.4 0.6 0.8 1.0 X fo Figure 1.5 The effect of variations in logKp e on lnK^ as predicted by the f i r s t - d i s s o c i a t i o n model for the hypothetical, case in which the o l i v i n e s o l i d solution i s i d e a l , (a) lnK^ vs Xf o at 600°C, 2kb. 30 0 -- 1 -Q - 3 -- 4 lnKE=-1.0 logKM g=-2.0 logK F e ALK r 3 . 0 +1.0 -2.50 -2.0 0.0 -2.00 -1.5 -0 .5 -1.75 -1.0 -1.0 -1.50 600°C 2kb Ideal Olivine: X =0.5 T 0.0 1.0 T 0.5  1.5 2.0 Total Molality 2.5 Figure 1.5 (b) l n kD vs mT at 600°C, 2kb. 31 To apply the f i r s t - d i s s o c i a t i o n model to the o l i v i n e ion-exchange data, i t was necessary to establish equation (3) f i t parameters for logKp e. The f i t parameters required to reproduce the entire data set were calculated by simultaneous regression of logKF e f i t parameters and o l i v i n e s o l i d solution f i t parameters using experimental P, T and f i n a l as independent variables and lnK^ as the dependent var i a b l e . The calculations were performed with a 'derivative-free' non-linear regression program c a l l e d BMDPAR: a FORTRAN program d i s t r i b u t e d by BMDP S t a t i s t i c a l Software, Inc. Unconstrained regression of the experimental data produced u n r e a l i s t i c f i t parameters for Kp e. In p a r t i c u l a r , a negative temperature c o e f f i c i e n t was calculated implying a temperature variation of logKF e which i s in contrast to a l l other e l e c t r o l y t e d i s s o c i a t i o n constants for which data e x i s t . A review of the data in figure 1.6 shows why th i s result was ine v i t a b l e . Regression produces a moderate positi v e ALK at 450°C, 2kb and a moderate negative ALK at 600°C, 2kb. Satisfying both of these would give logKF e a positive slope on figure 1.4. More reasonable values for logKF e f i t parameters were established by combining general constraints provided by s o l u b i l i t y studies, the o l i v i n e ion-exchange data, and the examples set by dis s o c i a t i o n constants measured for other chloride e l e c t r o l y t e s . F i t parameters for logKF e were hand calculated according to the following c r i t e r i a : 32 FeCl2 i s e s s e n t i a l l y associated at 800°C, 2kb (logKp e < -3.0). ALK < 0.0 at 600°C, 2kb. ALK > 0.0 at 450°C, 2kb. ALK * 0.0 at 600°C, 4kb. The res u l t i n g f i t parameters are a=-2.1, b=l000 and c=6.0. The s o l i d curves on figure 1.6 i l l u s t r a t e the behavior of the f i r s t - d i s s o c i a t i o n model using these logKF e parameters and Model B for the o l i v i n e s o l i d solution (described below). The behavior of the f i r s t d i s s o c i a t i o n model, as depicted in figure 1.6, s a t i s f i e s the low m^  data in form only; missing several of the 1a brackets. In an attempt to improve the a b i l i t y of the aqueous model to f i t the low mT data, two of the more obvious extensions of the f i r s t - d i s s o c i a t i o n model were added. (1) The 'extended' mean ionic a c t i v i t y c o e f f i c i e n t expression of Helgeson et a l (1981) was introduced using their b values calculated for MgCl2. (2) The second d i s s o c i a t i o n e q u i l i b r i a were added using a K2FeCl2 having a relationship to K2MgCl2 following the same ALK c r i t e r i a used in c a l c u l a t i n g K,FeCl2. Neither of these two extensions was found to s i g n i f i c a n t l y improve correspondence of the aqueous model to the low mT data. Discrepancies between the model and the data at low mT could be attributed to additional aqueous species not considered in the model. There is evidence that other species must, in f a c t , be present. For instance, the 33 0 -\£ - 1 - 2 - 3 0.0 T h 0.5 450°C 2kb Xfo =0.4 t 450°C 1kb X f o =0.4 1 1 600°C 1kb X f o =0.5 1.0 1.5 2.0 Total Molality 2.5 Figure 1.6 lnK^ vs mT for i s o t h e r m a l - i s o b a r i c - i s o X ^ subsets of the ion-exchange experiments. The symbols marking each experimental measurement point in the d i r e c t i o n of approach toward equilibrium. The measurement i t s e l f i s at the center of the symbol and the length of the symbol represents ±1a in l n h w . Minor deviations in measured X£ from the stated D ro constant value have been corrected for by adjusting lnKD parallel to Model B (see text for description of the models). The s o l i d l ines i l l u s t r a t e lnKQ predicted by the f i r s t - d i s s o c i a t i o n model combined with Model B. (a) Data at 450°C (Ikb and 2kb) and 600°C d k b ) . 34 0 -Q ^ - 1 - 2 -- 3 600°C 4kb V A A 4 1— I I 1 600°C 2kb Xf o =0-5 0.0 0.5 r 1.0 1.5 2.0 T o t a l M o l a l i t y 2.5 Figure 1.6 (b) Data at 600°C (2kb and 4kb). 35 Cl/(Mg+Fe) ratios in table 1.1 average s l i g h t l y less than 2.0 indicating that non-chloride species of aqueous Mg and Fe must be present. Also, the formation of minerals more si l i c e o u s than o l i v i n e during the ion-exchange experiments indicates that MgO and FeO (as components) have a higher s o l u b i l i t y in the aqueous solution than S i 02. The equation (3) f i t parameters for K,FeCl2 should be useful as an empirical first-approximation. The observable shortcomings of the f i r s t - d i s s o c i a t i o n model indicate that further research i s needed in order to understand the role of the chloride f l u i d in these and other chloride ion-exchange experiments. Such research could include independent measurement of K,FeCl2 and K2F e C l2, i d e n t i f i c a t i o n and concentration measurement of non-chloride species, and measurements of lnKD (ion-exchange) as a function of mT at other temperatures and pressures. THE SOLID SOLUTION: A s i n g l e - s i t e stoichiometric s o l i d solution model was deemed appropriate for the Mg-Fe o l i v i n e s o l i d solution since long range ordering of Mg and Fe in o l i v i n e has been shown to be minor or absent (see Brown, 1980, for review of o l i v i n e s i t e occupancy). A 'Margules' type of formulation was chosen for the sake of comparison. It has been widely applied to s i l i c a t e solutions following i t s introduction to the geologic l i t e r a t u r e by Thompson(1967; see also Grover, 1977; Berman and Brown, 1984). It i s also the formulation 36 used in most Mg-Fe o l i v i n e s o l i d solution studies previously published. A second order, 'symmetric* Margules formulation was found most appropriate to model the olivine-aqueous chloride exchange equilibrium data presented here. If we adopt the f i r s t - d i s s o c i a t i o n model for the aqueous solution and consider, for the moment, the case in which MgCl2 and FeCl2 are both f u l l y associated, we can write: 7 f o KD = KE — ( 1 9 )  7f a Taking the natural logarithm of both sides and substituting in Margules expressions for ln7 we have: lnKD = l n KE +l / R T [ ( l - Xf o) M WM g + 2Xfo(WFe-WMg)) -X|o(WF e +2(l-Xf o)(WM g-WF e))] (20) for a t h i r d order, 'asymmetric' Margules formulation and: lnKD = lnKE + WG(1-2Xfo)/RT (21) for the symmetric model. As i l l u s t r a t e d in figure 1.3, equation (21) i s linear in X^Q and equation (20) describes a curved l i n e in lnK_. vs X. .A review of the d i s t r i b u t i o n of D f o data points and their standard errors on figure 1.8 shows that a function linear in X^Q i s the highest order polynomial in X^Q that the data seem to require. This 37 judgement i s not affected by inclusion of p a r t i a l d i s s o c i a t i o n in the aqueous model since, as shown in figure 1.5, the influence of the f i r s t - d i s s o c i a t i o n model on lnKQ i s only weakly dependent on X^Q, and that dependence i s e s s e n t i a l l y linear over intermediate values of X^Q. Regression of the Margules parameter and AG0 of the exchange reaction (equation (5)) for isothermal-isobaric portions of the data produced the values l i s t e d in table 1.3. The thermodynamic parameters presented are a l l molar quantities for the formula units used in equation (5). The data set as a whole can be adequately f i t using the standard linear expression for AG? AG§ = AH5- TAS§+ PAV§ (22) and i t s equivalent for V?G WG = WH - TWS + PWy (23) but only i f pre-existing data outside the P-T conditions of the present study are ignored. However, only equation (23) need be modified to s a t i s f y pre-existing data since no other data exist which would constrain equation (22) at s u p e r c r i t i c a l pressures and temperatures. Figure 1.7 compares values from table 1.3 (2kb isotherms plus the 1kb, 450°C isotherm) with published values of and published stoichiometric solution models. The data from Obata et al(l974) are the product of Table 1.3. Isothermal-isobaric regression results for the ion-exchange reaction and the stoichiometric o l i v i n e solution model. See also equations (5), (6), and (21). P(bars) T(°C) AG|(J) (1a) WG(J) (1a) 1000 450 1 580 (520) 7770 (1300) 1 000 600 1 0970 (490) 3200 (1200) 2000 600 7730 (280) 5920 (560) 4000 600 2050 (610) 6280 (1400) 2000 725 1 4280 (300) 3720 (500) 2000 800 1 721 0 (340) 1750 (500) compilation and re-interpretation of olivine-orthopyroxene ion-exchange equilibrium data assuming an id e a l l y double-sited solution model for the orthopyroxene. The experimental data compiled by Obata et al(l974) were a l l collected at 1atm excepting the data at 1073K and 1173K which were co l l e c t e d at 500bars (Medaris, 1969). W_ values from Kawasaki and Matsui(1977) and O'Neil and Wood(l979) are based upon olivine-garnet exchange e q u i l i b r i a studied at 50kbar and 30kbar respectively. Kawasaki and Matsui(1983) experimentally studied garnet-orthopyroxene-olivine exchange e q u i l i b r i a at 50kbar. The second order Margules model from Andersen and Lindsley(1981) is based on oli v i n e - i l m e n i t e exchange e q u i l i b r i a (Andersen and Lindsley, 1979) and ilmenite-magnetite exchange e q u i l i b r i a (Lindsley, 1978). Andersen and Lindsley(1979) conducted exchange equilibrium 39 14000 -12000 -10000 -CD 8000 -4000-2000-0 --2000 E( 1980a) W M g K&M(1977) K&M(1983) 0&W(1979) I 400 600 — , 1 r 1 1 800 1000 1200 1400 1600 1800 Temperature (K) Figure 1.7 A compilation of the most recent and most comprehensive measurements of and Margules solution models for Mg-Fe o l i v i n e s . The diamonds represent values from olivine-orthopyroxene ion-exchange experiments as compiled and re-interpreted by Obata et a l . ( l 9 7 4 ) . The v e r t i c a l bars below 1200K represent 1a error bars about W^  values produced in the present study by regression of isothermal-isobaric subsets of the data (see table' 3). The remaining authors have been abbreviated as follows: E = Engi, A&L = Andersen and Lindsley, K&M = Kawasaki and Matsui, O&W = O'Neill and Wood. 40 experiments at both latin (700 to 980°C) and 13kb (800 to 900°C). The third-order Margules model of Engi(1980a) is based upon the olivine-orthopyroxene data as interpreted by Obata et al(l974) and oxide-melt solution calorimetry by Wood and Kleppa(1981). The solution models of Engi(1980a) and Anderson and Lindsley(1981) are the most sensible guidelines for the high temperature behavior of the o l i v i n e s o l i d solution at r e l a t i v e l y low pressures. They agree"quite c l o s e l y with each other above 1000K, where most of the data were c o l l e c t e d . A solution model consistent with the present study and these two published models would be characterized by 3Wg/3T < 0 and 92WG/9T2 > 0 such that WQ and 3WQ/9T both approach zero at about 1600K where the s o l i d solution i s e s s e n t i a l l y i d e a l . This agrees with the concept that the s o l i d solution should asymptotically approach ideal behavior at a s u f f i c i e n t l y high temperature. The published data on figure 1.7 which are obviously inconsistent with t h i s generalization are a l l the product of high pressure exchange experiments with Fe-Mg garnets. Their inconsistency could stem from inappropriate assumptions about the garnet s o l i d solution or from a substantial pressure dependence of the o l i v i n e s o l i d solution properties, a p o s s i b i l i t y discussed below. Variation of WH and Wg with temperature must be introduced i f the s o l i d solution model is to follow the above guidelines. One way to accomplish this i s to postulate 41 a constant excess heat capacity as did Engi(1980a) WH = W 5 + W C ( T " T 0 ) ( 2 4 ) Ws = W°+ Wcln(T/T°) (25) Regression of W ° , W° , Wc and Wv using the data in table 1.1, choosing T°= 298K and constraining WG to be 0.0 at 1600K produced the parameters l i s t e d as Model A in table 1.4. The value of V?v produced by regression (Model A) i s poorly constrained by the data and is seen to be unacceptably large when compared to the 0.13J/bar AV between f o r s t e r i t e and f a y a l i t e , and when compared to Wv values derived from unit c e l l refinements. Published c e l l dimension studies of synthetic o l i v i n e s constrain Wv at STP to be 0.007±.005J/bar (Akimoto and Fujisawa, 1968), 0.0l5±.004J/bar (Fisher and Medaris, 1969) and 0.011±.001J/bar (Schwab and Kustner, 1977). Calculating the Wv necessary to bring the high pressure garnet-olivine studies into consistency with low pressure studies at similar temperatures (assuming that the mixing properties of Fe-Mg garnet are independent of pressure; Kawasaki and Matsui, 1977) yields a value of 0.l2J/bar. If Wv i s assumed to have l i t t l e or no dependance on pressure, t h i s too must be rejected as too large, indicating that o l i v i n e mixing properties calculated by O'Neill and Wood(1979) and Kawasaki 42 Table 1.4. Regressed f i t parameters for the ion-exchange reaction and the stoichiometric s o l i d solution model. See equations (5) , (6), and (21) -(25) . Model: A B (la) AHg(J) 33500 -33400 (2000) AS|(J/K) -53.3 -53.3 (2.3) AV?(j/bar) -2.74 -2.75 (0.2) wH(j) 35700 37700 (5400) WS(J/K) 46. 1 48.7 (7.0) WC(J/K) -27.4 -29.0 (4.1 ) Wy(J/bar) 0.16 0.011* (0.6) * Fixed value; not regressed and Matsui(l977, 1983) are truely inconsistent with the low pressure studies. The study by Schwab and Kustner employed by far the largest number of o l i v i n e compositions and attained the highest measurement accuracy. However, the o l i v i n e s they studied were a l l synthesized at temperatures greater than 1000°C. Their measurements may not apply equally well to o l i v i n e s annealed at the lower temperatures included in the present study. In order to check t h i s p o s s i b i l i t y , unit c e l l refinements were performed on the product o l i v i n e s from ion-exchange experiments conducted at 450°C and 1kb. Also included were an endmember f o r s t e r i t e annealed at 800°C, 2kb and an endmember f a y a l i t e synthesized at 450°C, 4kb. Powder XRD techniques were employed using a P h i l i p s PW1710 d i g i t a l 43 d i f f T a c t o m e t e r e q u i p p e d w i t h a CUKq source and a g r a p h i t e m o n o c h r o m a t o r . L e a s t - s q u a r e s r e f i n e m e n t of u n i t c e l l p a r a m e t e r s was a c c o m p l i s h e d w i t h a USGS FORTRAN IV program (Evans et a l , 1963). Table 1.5. O l i v i n e c e l l parameters derived from powder XRD peaks i n the 40' to 75' 20 range. (CuKa, s y n t h e t i c spinel i n t e r n a l standard) RUN* INITIAL f o FINAL f o a(A) b(A) c(A) V( A' ) * OF PEAKS OS- 16 1 OOO 1 OOO 4 . 7547(4)* 10.1985(8) 5 .9816(5) 290.06(3) * * 22/8 147 1 OOO 0 984 4 .7552(2) 10.1981(5) 5 .9812(2) 290.05(2) 12/5 146 0.710 0. 728 4 7763(3) 10.2806(9) 6 .0154(4) 295.38(3) 17/8 143 0. 400 0. 455 4 .7977(2) 10.3642(5) 6 .0476(3) 300.72(2) 22/ 10 142 0. 400 0. 338 4 .7990(3) 10.3670(6) 6 0481(3) 300.90(2) 25/ 1 1 145 0.104 0. 163 4 . 8153(2) 10.4479(7) 6 .0780(3) 305 78(2) 21/16 132 0.000 O.OOO 4 8205(4) 10.4758110) 6 .0881(6) 307.44(4 ) 18/7 In parentheses i s one standard e r r o r of regression as ap p l i e d to the l a s t s i g n i f i c a n t d i g i t l i s t e d . K peaks / CL I K peaks ot i Comparing the c e l l parameters of oli v i n e s taken from a bracketing pair of exchange runs (each having the same i n i t i a l o l i v i n e composition) indicated that their XRD signature was dominated by an o l i v i n e core composition i d e n t i c a l to the i n i t i a l composition. Since the contribution of the rim composition to XRD peak positions could be anticipated to be greatest at low angles, the c e l l refinements were repeated using only peaks above 4O°20. The results are l i s t e d in table 1.5. Note that the c e l l parameters of o l i v i n e s from runs 142 and 143 are almost indiscernable from each other despite rim compositions more than 0.1 X, apart. Regression of unit c e l l volume (using 44 i n i t i a l o l i v i n e compositions) to a quadratic in X^a, for the sake of dir e c t comparison with Schwab and Kiistner's regression, resulted in V(A3)=290.04(±.04) + l8.8(±.2)Xf -1.4(±.2)X| . This equation and the VE X implied by i t i s indiscernable from that of Schwab and Kiistner (1977) . The results of regression of the remaining model parameters while holding Wv constant at O.OlU/bar are also presented in table 1.4. The s o l i d l i n e s on figure 1.8 are calculated from Model B. 45 •1-^ - 2 -- 3 -- 4 J L 2m Chloride 600°C 2kb 0.0 0.2 800°C 2kb 0.4 0.6 0.8 1.0 X fo Figure 1.8 lnK^ vs : 2m chloride ion-exchange data and curves calculated with Model B combined with the f i r s t - d i s s o c i a t i o n model with the same values of T, P and mT« See figure 1.6 for explanation of symbols, (a) Data at 600°C (2kb) and 800°C (2kb). 46 Figure 1.8 (b) Data at 450°C (1kb) and 725°C (2kb). -1 1 r 1 1 |-0.0 0.2 0.4 0.6 0.8 1.0 Figure 1.8 (c) Data at 600°C (Ikb) and 600°C (4kb). 48 DISCUSSION THE CHLORIDE: The remaining uncertainties in the behavior of the aqueous chloride solution render mineral-aqueous chloride ion-exchange experiments such as these of limited use in determining the absolute value of endmember and s o l i d solution properties for a single mineral. U n t i l these uncertainties are removed (by independent research) t h i s experimental medium i s best used for comparison of mineral properties using the aqueous chloride as a 'common denominator'. If the f i r s t - d i s s o c i a t i o n model i s correct in form, then uncertainties in the d e t a i l s of t h i s model should have l i t t l e e f f e ct on the s o l i d solution model derived from the ion-exchange experiments. The 'excess' properties of the s o l i d solution are derived only from the v a r i a t i o n of KQ with (mineral) composition and not from the absolute value of KD» Figure I.5a shows that, for aqueous e l e c t r o l y t e solutions resembling the f i r s t - d i s s o c i a t i o n model, KD is at most weakly dependent on the composition of the aqueous solution (at constant t o t a l m o l a l i t y ) . The strongest effect of uncertainties in the f i r s t - d i s s o c i a t i o n model i s in the value of Kg, the equilibrium constant for the model ion-exchange reaction. Figure I.5b shows that t h i s effect i s 49 minimized at high t o t a l m o l a l i t i e s . As a result of this uncertainty in , endmember thermodynamic properties for the s o l i d solution could not be unambiguously calculated from the ion-exchange equilibrium data. This would be true even i f the thermodynamic properties of the endmember neutral chloride species had been determined independently. The f i r s t - d i s s o c i a t i o n model assumes that Mg and Fe endmembers of otherwise i d e n t i c a l aqueous species interact i d e n t i c a l l y with the solvent. It also assumes that these Mg and Fe endmember species interact i d e a l l y with each other. If either of these assumptions is in e r r o r , then Mg-Fe s o l i d solution properties calculated d i r e c t l y from the ion-exchange experiments w i l l be in e r r o r . In spite of a l l of these uncertainties, aqueous chlorides s t i l l have u t i l i t y as an experimental medium for establishing mineral properties. The use of a chloride aqueous solution as an ion-exchange phase reduces the d i f f i c u l t i e s inherent in performing the experiments: synthesis of starting materials; attainment of equilibrium; measurement of compositions. If mineral-chloride exchange e q u i l i b r i a are determined separately over the same range of P and T (and mT) using the same binary solution of aqueous chl o r i d e s , then the r e l a t i v e thermodynamic properties of these minerals can be determined without dependence on how the aqueous solution i s treated. If the absolute properties of one of these minerals i s known from independent evidence, then the absolute properties of the remaining phases can be 50 estimated. THE OLIVINE-. Figure 1.9 i l l u s t r a t e s the temperature dependence of W^  and WH for Model B at 1bar. Comparison with the theoretical unmixing l i m i t for a symmetrical Margules formulation (W^  = 2RT) shows that Model B predicts a solvus c r i t i c a l point at about 400°C. Although comparison of thi s model with the 2molal ion-exchange data (figure 1.8) i s favorable, t h i s solution model may s t i l l be judged inadequate: Functional Form'. The model for W^, smoothly and more-or-less asymptotically approaches zero at high temperatures. For a s o l i d solution approaching ' i d e a l ' behavior as a high temperature l i m i t , Wu should have a similar functional form. Calorimetry. The values of Wu predicted by Model B are inconsistent with a l l of the calorimetric constraints on Wu. To review; HF calorimetry at 345K found no evidence of excess enthalpy of mixing (±1400J in W^ ; Sahama and Torgeson, 1949), Pb-borate melt solution-calorimetry at 970K was interpreted to be consistent with an asymmetric solution model with Wu(Mg) * 4200J and W„(F e ) * 8400J (±2500J in Wu; Wood and Kleppa, 1981), and (Na,Li)-borate melt-calorimetry at 1180K did not detect an enthalpy of mixing s i g n i f i c a n t 51 18000 -14000 -10000 -0) 6000 2000--2000 -i 1 r 400 600 800 1000 1200 1400 1600 1800 Temperature(K) Figure 1.9 and WH calculated using the f i t parameters l i s t e d under Model B in table 4. See also equations (23) through (25). 52 compared to the error brackets of their methods (±4000J for WH; Thierry, et a l , 1981). Even compared to the larger of the two WH values calculated by Wood and Kleppa(1981), Model B d i f f e r s by a factor of 2. At 1180K, Model B i s s t i l l a factor of 2 away from consistency with calorimetry. The HF calorimetry i s grossly inconsistent with Model B, but i t was performed at a temperature far from the range covered by the present study. On the other hand, the calorimetry of Wood and K l e p p a ( l 9 8 l ) and Thierry et a l ( l 9 8 l ) was performed at temperatures overlapping the present study and should ide a l l y be included as constraints on the o l i v i n e solution model. These remaining problems are addressed in the next chapter. I I . Application to Orthopyroxene, Orthoamphibole and Talc and Comprehensive Analysis INTRODUCTION The experimental methods and theoretical models established in the study of synthetic Fe-Mg o l i v i n e s have been applied to the study of 3 other synthetic Fe-Mg s i l i c a t e s : orthopyroxene, orthoamphibole, and t a l c . These minerals can be seen to be l o g i c a l choices for pragmatic application of the Fe-Mg chloride exchange equilibrium technique based upon consideration of experimental and theoretical p r a c t i c a l i t i e s and the need for p r a c t i c a l application of the results to natural assemblages. Although the the o r e t i c a l tools being used can be applied to multicomponent s o l i d (and aqueous) solutions, the study of multi-component systems i s best preceeded by thorough understanding of the binary subsystems. Therefore, components outside the Mg0-Fe0-Si02-H20-HCl system are undesirable u n t i l the properties of minerals within this system are understood. In the previous chapter, theoretical interpretation of the role of the aqueous solution in olivine-aqueous chloride ion-exchange experiments has shown that the properties of the Fe-Mg chloride aqueous solution are s t i l l incompletely understood. Therefore application of the technique is best r e s t r i c t e d to the P-T regime of the o l i v i n e ion-exchange experiments. Fe-Mg orthopyroxenes, 53 54 orthoamphiboles and ta l c s have already been shown to a l l be: (1) possible to synthesize within the MgO-FeO-Si02-H20 system (Greenwood, 1963; Hellner et a l , 1965; Forbes, 1969; Popp et a l , 1976); (2) stable over at least a portion of the P-T range covered in the o l i v i n e ion-exchange experiments (Greenwood, 1963; Forbes, 1971a; Ravior and Hinrichsen, 1975; Chernosky, 1976; Popp et a l , 1977; Chernosky and Autio, 1979; Chernosky et a l , submitted for publication); (3) s u f f i c i e n t l y common in natural assemblages to be referred to as 'rock forming minerals' (Deer et a l , 1966). This system of 4 minerals (including o l i v i n e ) has the unusual d i s t i n c t i o n of being represented in nature as major minerals in rocks containing only very minor amounts of components outside the synthetic subsystem: i . e . metamorphosed peridotites (see Trommsdorff and Evans, 1974). The orthopyroxene Fe-Mg s o l i d solution has received considerable attention in the l i t e r a t u r e . However, there i s s t i l l some u t i l i t y in further experimental and theoretical scrutiny of Fe-Mg orthopyroxenes. The bulk of the published studies are directed toward documentation, experimental c a l i b r a t i o n and theoretical modelling of Fe-Mg i n t e r c r y s t a l l i n e exchange between orthopyroxene and Ca-rich clinopyroxene, o l i v i n e , or garnet (see Deer et a l , 1978; Sack, 1980). The i n t r a c r y s t a l l i n e exchange of Fe and Mg between the M1 and M2 octahedral s i t e s is also well documented (see Appendix G). The experimental studies of i n t e r c r y s t a l l i n e ion-exchange have few contributions to 55 offer for temperatures below 800°C. Sack(1980), in formulating a solution model consistent with both the i n t r a c r y s t a l l i n e and i n t e r c r y s t a l l i n e data, was forced to include several approximations and assumptions. The choice of orthorhombic over monoclinic Fe-Mg amphiboles i s not necessarily the most pragmatic i f based upon natural occurrences alone. Occurrences of natural anthophyllites (low in Al and a l k a l i s ) only span about 35% of the composition range between Mg and Fe endmembers (Rabbit, 1948; Deer et a l , 1963). Natural cummingtonites cover 85% of the Fe-Mg solution (Deer et a l , 1963; Klein and Waldbaum, 1967; Rice et a l , 1974). The decision to study Fe-Mg orthoamphiboles i s based upon experimental f e a s i b i l i t y and maximum u t i l i t y . It has been proven possible to synthesize orthorhombic amphiboles over 86% of the Fe-Mg s o l i d solution (Popp et a l , 1976). Synthesis of pure Fe-grunerite has only been accomplished with d i f f i c u l t y and low yields (Forbes, 1971b). Synthesis of intermediate Fe-Mg cummingtonites has only been accomplished by adding small amounts of CaO (Schiirmann, 1966; Cameron, 1975); an undesired additional component. Phase equilibrium experiments delineating mineral s t a b i l i t i e s in the Mg end-member system have a l l been conducted using orthorhombic amphiboles (Fyfe, 1962; Greenwood, 1963; Chernosky and Autio, 1979; Chernosky et a l , submitted). Thermodynamic characterization of the orthoamphibole Fe-Mg s o l i d solution i s thus a dir e c t extension of the Mg endmember studies. 56 The range of Fe-Mg compositions covered here in studying orthoamphibole and t a l c i s considerably wider than the population of natural compositions. The u t i l i t y of this approach is to maximize the 'leverage' the data has on the s o l i d solution properties. This approach also w i l l help define the true s t a b i l i t y of each mineral as opposed to the probability of i t s occurrence based upon the d i s t r i b u t i o n of natural bulk compositions. E X P E R I M E N T A L T E C H N I Q U E S The hydrothermal apparatus, starting materials, ion-exchange experimental techniques, and methods employed for compositional measurements are v i r t u a l l y i d e n t i c a l to those employed in the olivine-aqueous chloride ion-exchange study. Any differences are noted. The reader i s referred to Chapter I and the appendices for d e t a i l s . SYNTHESES: In contrast to the Fe-Mg o l i v i n e syntheses, a l l syntheses employed hydrothermal techniques. In most cases an aqueous solution of Mg-Fe chlorides was used as a flux with the intent of increasing reaction and r e c r y s t a l l i z a t i o n rates. Orthopyroxene: Oxide mixes on orthopyroxene bulk compositions at X ° ^x = 1.0, 0.8, 0.6 and 0.4 were sealed 57 into gold capsules along with a 2molal aqueous chloride f l u x . The capsules were kept at 800°C (±10°) and 2kb for 16 days. The synthesis products were a l l 'coarsely' c r y s t a l l i n e with individual prismatic grains up to 4mm long. XRD patterns for these products contained only peaks attributable to orthopyroxene. Optical examination revealed traces of o l i v i n e or quartz. A portion of each synthesis was set aside for microprobe analysis and the remainder was ground to a grain size <1(DMm. Using standard analysis techniques, microprobe analyses of the intermediate composition synthesis products revealed that most grains were s l i g h t l y zoned. Averages of 15 evenly d i s t r i b u t e d analyses gave f i n a l compositions at 0.370±0.025, 0.570±0.024 and 0.770±0.025 (X°Px±1a). The discrepancy between mix compositions and f i n a l compositions i s due to ion-exchange with the aqueous chloride f l u x . Orthoamphibole: Six orthoamphibole compositions from X^ *"*1 = 0.1 to 1.0 were synthesized using a variety of synthesis st r a t e g i e s . Appendix F contains the d e t a i l s of the synthesis runs and characterization of the products. The techniques employed for phase characterization include powder XRD, electron d i f f r a c t i o n and high magnification TEM imaging. The synthesis products are a l l f i n e l y f i b r o u s . The individual accicular grains are up to 80Mm long and seldom greater than 1 jum in diameter. Chemical analysis of the aqueous run f l u i d enabled product amphibole compositions to 58 be accurately calculated by mass-balance. Unit c e l l refinements of the synthesis products revealed discrepancies in c e l l dimensions (primarily the a-repeat) when compared to natural anthophyllites. Chain-stacking disorder i s proposed as the primary cause of the c e l l dimension discrepancies. The TEM study q u a l i t a t i v e l y supports t h i s theory. Talc: Four ta l c compositions were synthesized at 2kb using tal c a -Imolal aqueous chloride f l u x . Mix compositions at XMg 0.5, 0.7, 0.9, and 1.0 were heated at 450, 525, 610 and 700°C respectively. Synthesis durations ranged from 7 days for the Mg endmember to 16 days for the most Fe-rich composition. The synthesis products were a l l very fine grained (<5um). Powder XRD patterns contained only talc peaks. Optical examination revealed traces of quartz as the only impurity in a l l synthesis products. A sample of each intermediate composition t a l c was digested in HF + HC10„ and analyzed for Fe and Mg with standard flame atomic absorption talc techniques. The measured f i n a l compositions are 0.531, 0.740, and 0.926 (±0.005). ION-EXCHANGE EXPERIMENTS: The techniques employed in conducting the ion-exchange experiments are i d e n t i c a l to those employed in the o l i v i n e study excepting the separation of run f l u i d from talc and orthoamphibole run products. The high surface area and high porosity of these experimental charges prevented direct 59 extraction of the aqueous f l u i d by centr i f u g i n g . Following each ta l c and orthoamphibole ion-exchange experiment the capsule was cleaned, cut open with a length-parallel cut, and placed in a centrifuge v i a l containing 700yl of water. An ultrasonic bath was used to ensure thorough washing of the charge. After removing the empty capsule, the v i a l contents were centrifuged and the supernatant solution was drawn off for a n a l y s i s . For each mineral, the ion-exchange experimental temperatures were r e s t r i c t e d to a range in which the mineral is stable (or persistently metastable) over at least 50% of i t s Fe-Mg s o l i d s o l u t i o n . FINAL COMPOSITIONS'. Orthopyroxene: The products of orthopyroxene ion-exchange experiments generally included grains large enough for standard microprobe analysis. However, l i k e the synthesis products, these grains were found to be characterized by minor, but s i g n i f i c a n t , Fe-Mg zoning. Fi n a l compositions suitable for bracketing the ion-exchange equilibrium had to be obtained using an analysis technique which p r e f e r e n t i a l l y samples grain .edges. Both p a r t i c l e analysis and crystal-face analysis techniques were used. Orthoamphibole: F i n a l orthoamphibole compositions were 60 established with a powder XRD c a l i b r a t i o n curve for d0n0. This peak was chosen since i t depends only on the b c e l l repeat which, of the three orthogonal axes, exhibits the strongest dependence on Mg-Fe sub s t i t u t i o n . Although powder XRD c e l l refinements and electron microscopy indicate the presence of chain-arrangement f a u l t s in the synthetic starting materials, comparison with natural anthophyllites and other synthetics indicates that the fe-repeat i s not strongly affected by the presence of these f a u l t s (see Appendix F ) . Figure II.1 shows the d0^Q values derived from f u l l c e l l refinements of the synthetic starting materials. The c a l i b r a t i o n curve i s a least-squares f i t of a quadratic in x5"th to a l l but the datum at x5nth=0.9. Its formula i s Mg Mg rfo«o = 4.616 - 0.l85XM g + 0.049X^g. Individual peak measurements using d i g i t a l peak-seeking procedures and quartz as an internal standard are accurate to ±0.01°26 (CuKa, see also Appendix D). The f i n a l compositions are estimated to be accurate to ±0.03 in xf.nt^. The measured Mg values of d0llQ are l i s t e d in table I I . 1. The d o u o for the synthetic orthoamphibole at X^gt^1=0.9 does not conform to the c a l i b r a t i o n curve. Examination of this synthetic product with TEM has revealed an anomalously high amount of chain-width disorder. This type of structural defect w i l l not 'anneal out' since this would require a net-transfer reaction. F i n a l orthoamphibole compositions for experiments using this s t a r t i n g material were measured via acid-digestion plus atomic absorption, or calculated via 61 I 1 1 1 1 1 0.0 0.2 0.4 0.6 0.8 1.0 X M g (orthoamphibole) Figure II.1 Values of d0k0 measured for the synthetic orthoamphibole starting materials. The c a l i b r a t i o n curve i s a quadratic in XM g f i t to a l l measured values excepting that for the synthetic at XM o-0.9. 62 Table I I . 1 Orthoamphibole d 0 l l 0 values measured for ion-exchange run products. RUN# d0no(A) RUN# d0no(A) 255 4.540 307 4.505 257 4.531 308 4.502 309 4.551 249 4.500 310 4.597 250 4.535 31 1 4.598 251 4.518 252 4.558 280 4.530 253 4.544 281 4.499 254 4.501 282 4.508 283 4.559 305 4.501 284 4.537 306 4.500 285 4.504 mass-balance. Talc: F i n a l t a l c compositions were also measured using a powder XRD c a l i b r a t i o n . The d003 peak (one layer, t r i c l i n i c c e l l indexing) was chosen for c a l i b r a t i o n since the basal r e f l e c t i o n s were the only peaks which proved to be strong and sharp for a l l of the synthetic t a l c s . Since the d 0 o3 peaks were strong, sharp and i n t e n s i f i e d by preferred o r i e n t a t i o n , a 28 accuracy of ±0.003° was t y p i c a l l y obtained. Figure II.2 shows d003 values measured for the synthetic s t a r t i n g materials and a linear c a l i b r a t i o n curve with the formula d 0 0 3 = 3.1442-0.0278XMg. Also i l l u s t r a t e d are dQ03 values for several natural t a l c s and other synthetic t a l c s (see figure caption for references). The 63 XM9 (talc) Figure II.2 Measured values of t a l c cf0 0 3 and the linear c a l i b r a t i o n curve f i t to the synthetic sta r t i n g materials produced in the present study. The f i l l e d symbols represent these synthetics. The open symbols represent synthetic t a l c s from Chernosky et al(submitted) and Forbes(1969). The hatched symbols represent natural t a l c s from Rayner and Brown(l973) and Kioshi and Gilles(1979). 64 fi?003 values measured for the experimental run products are l i s t e d in table II.2. Fi n a l t a l c compositions are estimated to be accurate to ±0.03 in 3LV* . Table II.2 Talc d003 values measured for ion-exchange run products. RUN# d0o3(A) RUN# d003(A) 222 3.1291 238 3.1218 292 3.1267 239 3.1212 293 3.1230 286 3.1189 294 3. 1174 287 3. 1177 313 3.1233 289 3. 1279 314 3.1195 290 3.1256 237 3. 1255 DATA ANALYSIS Table II.3 l i s t s a l l of the data gathered for those ion-exchange experiments judged c r i t i c a l for bracketing the ion-exchange e q u i l i b r i a . The last column in table II.3 represents the results of the f i r s t step of the data analysis procedure. To f a c i l i t a t e comparison of the three c r y s t a l l i n e solutions with each other, and with the Mg-Fe o l i v i n e data, each exchange equilibrium was modelled as a reaction of Mg and Fe endmember minerals with the neutral chloride species. Each of these reactions was balanced with Table 11.3. Ion-exchange run data. A l l experiments were performed at 2kb. - - -INITIAL- - - MINOR - - - - - FINAL - - - - - - - - - - - - - - - - -SOLID FLUID PRODUCT SOLID . FLUID t RUN*1 T('C) HOURS X „ X,. mT PHASES X „ Cl/Mg+Fe X,. HOW 1 nK_. 1o InK. Mg Mg T Mg 3 Mg D D ORTHOPYROXENE EXPERIMENTS 264 680 719 0 .370 0 OOO 2 .0 0 . 06 1 0 .00 0 . 345 P -2 .09 0 . 12 - 1 . 92 265 680 719 0 . 370 O .500 2 .0 OA2 0 . 108 0 .00 0 .567 P -2 . 38 O .08 -2 .21 266 680 7 19 0 . 570 0 . 500 2 .0 OA 0 . 197 0 .00 0 .689 P -2 .20 0 .09 -2 .03 267 680 883 0 . 770 0 .000 2 .0 TA 0 . 183 0 .00 0 . 738 P -2 .53 0 . 12 -2 . 36 268 680 883 0 . 770 0 . 700 2 .0 0 . 440 0 .00 0 . 886 P -2 . 29 0 . 25 -2 . 1 1 269 680 883 1 .000 0. . 100 2 .0 0 . 4 16 0 .00 0 .937 P -3 .04 0 . 16 -2 .86 277 680 833 0 . 370 O. .212 2 .0 0 0 .063 1 .98 0. . 400 P -2 . 29 0 .08 -2 . 12 278 680 833 0. 770 0 412 2 .0 0 0 .258 1 98 0. 818 P -2 .56 0 .09 -2 . 38 279 680 833 1 . 000 0. 105 2 .0 0 . 345 1 97 0. 896 P -2 . 79 0 . 18 -2 . 62 228 800 300 0. . 370 0. 000 2 .0 0 0 .066 1 . .98 0. 466 F -2 . 51 0. 06 -2 . 35 229 800 300 0. 370 O. 300 2 .0 0 0 .092 0. 00 0. 527 F -2 40 0 06 -2 . 24 230 800 300 0. .570 O. 500 2 .0 0 0 195 1 . 96 0. 750 P -2 . 52 0. 09 -2 . 36 231 800 302 0. 770 0. 000 2 .0 0 0. 232 1 . 86 0. 788 P -2 . 51 0. 06 -2 . 35 232 800 302 0. 770 0. 700 2 .0 0 0. 296 0. OO 0. 874 P -2 . 80 0. 14 -2 . 64 233 800 302 1 . 000 0. 100 2 O 0. 542 0. 00 0. 966 P -3 . 18 0 16 -3 02 UH0AMPH1BOLE EXPERIMENTS 255 600 1475 0. 509 0. 000 2 . 0 0. 105 2 . 01 0. 465 X -2 00 0. 13 - 1 . 86 257 600 1475 0. 339 O. 700 2 . 0 0 0. 156 2 . 07 0. 517 M - 1 . 76 0. 06 - 1 . 61 309 600 904 0. 339 0. 210 2 . 0 0 0. 084 0. 00 0. 391 X - 1 . 95 0. 13 - 1 . 81 310 600 904 0. 102 0. 1 14 2 . 0 0 0. 020 0. 00 0. 105 X - 1 . 75 0. 32 - 1 . 6 1 Table 11. 3. (continued) - - -INITIAL- - - MINOR - - - - - FINAL - - - - - - - - - - - - - - - - -SOLID FLUID PRODUCT SOLID FLUID „ RUN* T('C) HOURS X,. X,. mT PHASES Xu Cl/Mg+Fe Xu HOW 1 nKn \a lnKn Mg Mg T Mg Mg u 0 31 1 600 904 0 . 102 0 OOO 2 .0 0 0 .018 0 .00 0 .093 X -1 . 72 0 . 36 - 1 . 58 252 650 1473 0 . 339 0 .000 2 .0 0 0 .049 2 .00 0 . 347 X -2 . 33 0 . 14 -2 . 16 253 650 1473 O . 339 0 .500 2 .0 OP 0 .077 1 .94 0 . 442 X -2 . 25 0 . 13 -2 .07 254 650 1473 0 . 509 0 . 700 2 .0 OP 0 .196 1 .98 0 . 787 X -2 . 72 0 . 18 -2 . 54 283 650 1550 0 . 339 0 . 208 2 .0 0 0 .059 1 .92 0 341 X -2 . 1 1 0 . 14 - 1 .93 284 650 1550 0 .509 0 .000 2 .0 0 0 .090 1 .87 0 . 485 X -2 .25 0 . 13 -2 .08 285 650 1550 0 . 753 0 . 101. 2 .0 0 0. . 177 1 .91 0 . 754 X -2 .66 0 . 17 -2 . 48 307 650 7 10 0 .907 0 .608 2 .0 TA 0. .566 0 .00 0 .939 W -2 .47 0 . 10 -2 . 27 308 650 7 10 O . 907 0 314 2 .0 TA 0. 347 0 .00 0 923 M -3 . 12 0. 15 -2 . 93 249 700 497 0. 509 0 . 500 2 .0 OL 0. 280 0 .00 0 . 798 X -2 . 32 0 . 19 -2 . 14 250 700 497 0. 509 0. .000 2 .0 0+OL 0. 096 0 00 0. 505 X -2 26 0 13 -2 .08 251 700 497 0. 753 0. .000 2 .0 0 0. 185 . 1. .95 0. 743 X -2 . 54 0. . 16 -2 . 36 280 700 833 0. 509 O. 311 2 0 OP 0. 103 1. 99 0. 543 X -2 . 34 0. 13 -2 . 16 281 700 833 0. 753 0. 4 13 2 . 0 OP 0. 259 2 . 17 0. 808 X -2 . 49 0. 20 -2 . .31 282 700 833 0. 753 0. 109 2 0 0. 182 1 . 99 0. 7 19 X -2 . 44 0. 16 -2 . 26 305 700 7 10 0. 907 O. 6 17 2 . 0 o. 591 0. 00 0. 934 M -2 . 28 O. 17 -2 . 09 306 700 710 0. 907 0. 259 2 . 0 0. 426 0. 00 0. 916 W -2 . 69 0. 08 -2 . ,50 ILC EXPERIMENTS 222 400 1361 0. 531 O. 000 2 . 0 OL 0. 115 1 . 92 0. 545 X -2 . 22 0. 13 -2 82 292 400 1627 0. 531 0. 308 2 . 0 0+OA 0. 21 1 0. 00 0. 630 X - 1 . 85 0. 14 -2 . 44 293 400 1627 0. 740 0. 206 2 . 0 0 0. 28 1 2 . 27 0. 761 X -2 . 10 0. 17 -2 . 68 294 400 1627 O. 926 0. 51 1 2 . 0 0 0. 515 2 . 34 0. 963 X -3 . 20 0. 84 -3 . 76 Table II.3. (continued) - - -INITIAL- - - MINOR - - - - - FINAL - - - - - - - - - - - - - - - - -SOLID FLUID PRODUCT SOLID FLUID „ RUN* T('C) HOURS X X m PHASES X Cl/Mg+Fe X HOW 1 nK 1o 1 nK 313 400 1907 0 . 740 0 .413 2 .0 0. 352 0 .00 0 . 753 X - 1 .72 0. . 17 -2 . 30 314 400 1907 0. .926 0 .677 2 .0 0. 655 0 .00 0 .887 X - 1 .42 0. 30 - 1 .97 237 500 7 18 0. . 531 0. . 500 2 .0 0 0. 207 1 .89 0 .671 X -2 .06 0. 14 -2 .04 238 500 7 18 0. 740 0 .000 2 .0 Q+OA 0. 124 0 .00 0 .804 X -3 .37 0. 20 ' -3 . 35 239 500 7 18 0. .740 0 .700 2 .0 0 0. 427 0 00 0 .828 X - 1 .87 0. 22 - 1 .85 286 500 161 1 0. .926 0 .615 2 .0 0. 479 1 .65 0. 911 X -2 . 4 1 0. 37 -2 . 39 287 500 1611 1 . OOO 0. 514 2 . O 0 0. 527 2 . 06 0. 952 X -2 . 88 0. 66 -2 .86 289 500 161 1 0. 531 O. OOO 2 . 0 OA+0 0. 1 19 2 . 00 0. 588 X -2 . 36 0 13 -2 . 34 290 500 1611 0. 531 0. 355 2 . 0 OA+0 0. 108 2 . 02 0. 669 X -2 .82 0. 14 -2 . 79 Method of f i n a l X,, determination: M=mass balance, S=standard microprobe, P=particle analysis, Mg F=crystal face a n a l y s i s , X=XRD c a l i b r a t i o n , W=wet chemistry. OA = orthoamphibo 1e, OP = orthopyroxene, TA = t a l c , and 0 = quartz. 68 one mole of Fe and Mg on each side of the reaction (see equation (5) in the previous chapter). For each experiment, the concentrations of the neutral chloride species were calculated using the f i r s t - d i s s o c i a t i o n model (see Chapter I ) . Given these concentrations, a new d i s t r i b u t i o n * c o e f f i c i e n t , , was calculated. The results of applying the same procedure to the 2molal o l i v i n e - c h l o r i d e data are l i s t e d in table II.4. The following thermodynamic analysis * of these KD values results in c a l c u l a t i o n of thermodynamic properties for a hypothetical (Mg,Fe)Cl2 phase (subject to any f a l l a c i e s of the f i r s t - d i s s o c i a t i o n model). Since the absolute properties of either end-member of t h i s hypothetical phase cannot be independently established, only the 'delta' properties, differences between the two endmembers, are calculated. Thermodynamic analysis of the ion-exchange data was made comprehensive by adding these data d i r e c t l y to a mineral data base (for the Si02-MgC—Fe-C-O-H system) established by Engi et a l ( l 9 8 4 ) . The generous cooperation of Dr. Martin Engi i s acknowledged. This computer data base system simultaneously considers net-transfer phase equilibrium data, calorimetric data, and both natural and experimental ion-exchange equilibrium data compiled from the l i t e r a t u r e . The general features of t h i s data base, as established by i t s authors, are as follows: 69 * Table II.4. LnKD values calculated for a l l o l i v i n e + 2m chloride ion-exchange experiments. RUN# * lnKD RUN# InK* RUN# * lnKD 1 42 -0. .40 1 45 0. .34 1 46 -1 .17 1 47 -3. .17 1 63 0, .05 1 65 0 .29 1 1 6 -1 , .55 1 22 -1 . .33 1 24 -1 .64 1 99 -1 , .08 200 -1 . .39 25 -0 .26 26 -0, .69 27 -o, .70 37 -1 .31 38 -1 , .57 39 -1, .64 40 -1 .41 41 -1 , .76 42 -1, .67 43 -1 .10 64 -1 , .85 66 -1. . 1 3 101 -0 .75 1 28 -0, .29 174 -1, .31 197 -0 .14 225 0, . 1 1 226 -o, .32 227 -0 .96 69 -1. .40 70 -1, .41 71 -1 .84 72 -2. .08 21 1 -1, .99 212 -1 .87 213 -1 , .72 75 -1, . 14 169 -2 .19 1 70 -2, .10 202 -1, .96 203 -1 .92 204 -2, .04 Computational Method'. The computational method i s based upon application of MINOS (Modular In-core Nonlinear Optimization System, Murtagh and Saunders, 1980). To generalize: a linear programming algorithm i s used to find a solution-set of thermodynamic parameters which i s i n t e r i o r to inequality constraints derived from net-transfer equilibrium brackets and inequality constraints bounding the a n a l y t i c a l error of calorimetric data (see Halbach and Chatterjee, 1982; Berman et a l , 1984). Then an i t e r a t i v e nonlinear 70 optimization procedure i s used to minimize the sum of squares of the residuals, for example, between calculated ion-exchange Kp's and the ion-exchange equilibrium data. Fe-Mg Solution Minerals'. Included are o l i v i n e , orthopyroxene, anthophyllite, t a l c , minnesotaite, cummingtonite and serpentine. Net-Transfer Equilibrium Constraints: 195 individual experimental brackets representing 20 d i f f e r e n t reactions are included. Bounds: 76 individual bounds on thermodynamic parameters are included. These bounds are derived from calorimetry, unit c e l l volume measurements and the o r e t i c a l considerations. I on-Exchange Data: Pressure, temperature, and compositions for 314 natural and experimental mineral pairs are included. However, to reduce the size of the computational task and to remove any redundancy, the data for each type of mineral pair has been grouped according to s i m i l a r i t i e s in P, T and composition. Each group is represented in the data base by a mean calculated from the individuals in the group. Each datum entered into the data base i s assigned a weight which i s 71 used by the optimization algorithm. These weights are calculated in proportion to the standard error inherent in each (average) value. Heat Capacities'. A heat capacity equation modified by Berman et al(l984) i s used. c = k0 + — + — + — (k,, k2 < 0) (26) P cpO'5 rp 2 rp3 Solid Solution Models: Symmetric Margules-type solution models are used throughout. For functional f l e x i b i l i t y , an excess heat-capacity with 3 f i t parameters is included in the formulation: C Q W = A + — + — (27) *-p i p 2 !J1« Ion-exchange data from the present study were added to the data base with procedures similar to those of the pre-existing system. For each isothermal-isobaric data set (for each mineral), groups of brackets spanning a limited * range of composition and.lnKD were averaged together. In * t h i s way the t o t a l set of lnKD data was reduced to 33 points. The established weighting scheme considers only 72 compositional scatter and a n a l y t i c a l errors. However, the error l i m i t s in pressure and temperature t y p i c a l of the present study are much narrower than those t y p i c a l of the natural ion-exchange data which dominate the pre-existing * data base. Accordingly, the weights entered for the lnKD averages were a r t i f i c i a l l y advanced by approximately a factor of 10. The constraints placed on the Mg-Fe solution phases pertinent to this study are as follows: Olivine: The o l i v i n e s o l i d solution model was constrained to l i e within the error bars of the high temperature calorimetry by Wood and Kle.ppa (1 98 1 ; approximated by w^= 8kJ±2kJ at 970K) and Thierry et a l ( l 9 8 l ; W°1=0±4kJ at 1180K). In addition, W ° ^ " and W ° ^ " were both constrained to rl \j aproach that of an ideal solution at 1600K. S p e c i f i c a l l y , W°"*" was constrained to be 0±100J and was constrained to 0±500J at 1600K. Orthopyroxene: The Mg-Fe orthopyroxene s o l i d solution was constrained within the calorimetric measurements of Chatillon-Colinet et a l ( l 9 8 3 ) . In l i g h t of orthopyroxene s i t e ordering rate studies (Besancon, 1981 and Besancon and Vaughan, submitted; see. also Appendix G) their calorimetric measurements indicating W°p x= 4kJ±4kJ at 1023K are interpreted here as the bulk W °p x of orthopyroxene in order-disorder equilibrium at the temperature of the 73 calorimetric experiments. In addition, a high temperature l i m i t was placed on the excess properties of the orthopyroxene s o l i d solution to ensure an approximate trend toward i d e a l i t y with increasing temperature. At 2000K both W°PX and W°PX were constrained between -3kJ and +3kJ. Constraints closer to OJ could not be j u s t i f i e d in l i g h t of the range of previous estimates for the orthopyroxene s o l i d solution properties (Kitayama, 1971; Navrotsky, 1971; Sack, 1980). AnthophylI ite: A correspondence between anthophyllite and the synthetic orthoamphiboles was assumed. In l i g h t of the limited temperature range of the natural and synthetic anthophyllite ion-exchange data, W^"*"*1 was constrained to be temperature independent. Talc: The wide brackets c h a r a c t e r i s t i c of the tal c - c h l o r i d e data cannot constrain the compositional * t a l c dependence of KD (see figure I I . 6 ) . Therefore WQ was constrained to be zero for the ta l c s o l i d s o l u t i o n . Minnesotaite was not treated as Fe-endmember t a l c . This approach is supported by known structural d i s t i n c t i o n s between talc and minnesotaite (Guggenheim and Bailey, 1982). In addition, chemical analyses of natural minnesotaite indicate a contrast in the amount of str u c t u r a l H20 (Blake, 1965). 74 The Chloride'. The (Mg,Fe)Cl2 solution was constrained to behave ide a l l y (Wghl= 0). MODEL 1: The numerical results of the data base calculations using the above constraints are l i s t e d in tables II.5 and II.6 for the phases pertinent to t h i s study. This set of * parameters w i l l be referred to as Model 1. Model lnK^ curves calculated from the parameters in these tables are compared with the experimental brackets in figures II.3 through II.6. Figure II.7 compares the solution models for the four s i l i c a t e s considered here. A number of inconsistencies can be i d e n t i f i e d between the solution set represented by Model 1 and the ion-exchange data. These inconsistencies are most easi l y described separately for each phase. * Olivine'. Figures II.3a and II.3b show that the model lnK^ is too weakly composition dependent at temperatures below 800°C to s a t i s f y the data. This behavior can be traced to 2 sets of constraints. The calorimetric constaints on n l i m i t s the rate at which W ° ^ " increases with decreasing temperature. In addition, the lack of compositional dependence assumed for the chloride solution prevents the * o l chloride phase from contributing to 91nKD/3XMg. Orthopyroxene'. It can be seen from figure II.4 that the Table II.5 Endmember thermodynamic properties for Model 1 NAME FORMULA H° H298 s' 0 298 k 0 k i k2 V (Jx10" " ) (d/*C) (J/' •c) (x10-3) (x10"5) (cm: " ) Fe-Ta1c Fe 3 S i «0.o(OH)J -4798 . 1 365 .00 678 .86 - 1 1700 -4683 17916 148 . 74 Talc MgoSi.0,D ( 0 H ) , -5897 .6 261 .86 664 . 1 1 -2147 -5187 -3274 136 .04 Fa y a l i t e F eIS i 0 » - 1476 .8 150 .60 248 .93 0 -1924 -1391 46 . 12 Forsteri te Mg;Si0« -2174. .0 94 .21 238 .64 0 -2001 -1 162 43 . 60 Ferros i1i te FeSiOi - 1 193 .6 95 .08 • 173 . 74 -946 -1367 1116 33 . 1 1 Enstat i te MgSiOj - 1545. . 7 66 . 17 166 .58 -2271 -1201 2792 31 .  34 Fe-Anthophyl1i te Fe.Si.On (OH) 2 -9425. 8 877 .49 1316 .31 -24235 -8445 35523 279. 05 Anthophy11i te Mg ?SiiOi J(OH): - 12069. 7 536 . 15 1219 .31 -34766 -5767 44009 265 . 77 FeCl 2 FeCl 2 0. 0 84 . 14 0 .0 0 0 0 28 . 25 MgCl 2 MgCl 2 -381 . 1 0 .0 0 .0 0 0 0 0. 0 76 Table II.6 Model 1 Margules parameters. A l l parameters pertain to 1 mole of Fe+Mg. Talc 01ivine Ortho- Antho- Chloride pyroxene p h y l l i t e W H(kJ) 0.0 44.63 1 4.27 2. 028 0.0 W S ( J / ° C ) 0.0 50.00 18.87 0.0 0.0 Wy(J/bar) 0.0 0.012 -0.016 0.0 0.0 A (J/°C) 0.0 26.41 -9.73 0.0 0.0 C (x1U-5) 0.0 -710.8 0.0 0.0 0.0 Q ( X 1 0 - 1 0 ) 0.0 923.2 0.0 0.0 0.0 correspendence between the thermodynamic model and the orthopyroxene- chlor ide data i s adequate i f the error bars on the data are expanded to 2a. However, there remains a problem with the orthopyroxene s o l i d solution model which i s more eas i l y explained using figure II.7 as an i l l u s t r a t i o n . S a t i s f a c t i o n of the chloride ion-exchange data requires a minimal contrast in between o l i v i n e and orthopyroxene. Sa t i s f a c t i o n of the natural and experimental olivine-orthopyroxene ion-exchange data generally requires a larger contrast in (M. Engi, pers. comm.). The high weight assigned to the chloride ion-exchange data brings about the minimum in W^1- W°?x at about 1000K. At higher temperatures, where most of the experimental olivine-orthopyroxene data l i e s , the two functions are forced to deviate. The magnitude of this deviation i s 77 0.0 0.2 0.4 0.6 0.8 1.0 X M g (Olivine) * Figure II.3 Comparison of o l i v i n e lnK^ data with curves calculated with Model 1 thermodynamic parameters, (a) A l l 2kb data plus 450°C (1kb) data. 78 Figure II.3 (b) Data at 600°C (1kb and 4kb). 79 0 --1 -* Q _E - 2 -- 3 --4 A 680°C 2kb A 800°C 2kb 680° A u n 800° v A TV \ 0.0 0.2 0.4 0.6 0.8 *Mg (Orthopyroxene) 1.0 Figure II.4 Comparison of orthopyroxene lnKQ data with curves calculated with Model 1 thermodynamic parameters. 8 0 0 -- 1 -* a S-2-- 3 --4 0.0 I 4 600°C 2kb A 650°C 2kb A 700°C 2kb 0.2 0.4 0.6 0.8 X M g (Orthoamphibole) 1.0 Figure II.5 Comparison of orthoamphibole lnKD data with curves calculated with Model 1 thermodynamic parameters. 81 -n « a J£ -2 - 3 ^ -4 0.0 A 400°C 2kb A 500°C 2kb 400fl 500s 0.2 T t 0.4 0.6 0.8 X M g (Talc) 1.0 Figure II.6 Comparison of t a l c lnK^ data with curves calculated with Model 1 thermodynamic parameters. 82 400 600 800 1000 1200 1400 1600 1800 Temperature (K) Figure II.7 Comparison of the four Model 1 W_ functions. ol Also included i s W calculated from Model 1 parameters. 83 limited by the constraints l i m i t i n g their excess functions at T>1600K. AnthophylI i t e: The lack of calorimetric data and net-transfer equilibrium constraints on Fe-anthophyllite permits the data reduction complete freedom to s a t i s f y the orthoamphibole-chloride data. However, lnKD models calculated for olivine-anthophyllite and talc-anthophyllite ion-exchange e q u i l i b r i a f a i l to s a t i s f y natural examples of these e q u i l i b r i a (M. Engi, pers. comm.). The mis-match in both cases i s consistent with a standard free-energy (at P and T) for Fe-anthophyllite which i s higher than that required by the data on the natural s o l i d s o l u t i o n . It i s proposed here that t h i s r e f l e c t s "a real-difference between s t r u c t u r a l l y ordered natural anthophyllites and the p a r t i a l l y disordered synthetic orthoamphiboles employed in this study (see Appendix F ) . MODEL 2: In an e f f o r t to remove some of the remaining inconsistencies between the data and the thermodynamic model, the data-base cal c u l a t i o n s were repeated with one major constraint removed. The assumption of ideal mixing in the chloride solution was removed since there i s no physical data which d i r e c t l y supports this constraint. However, the chloride solution model was not l e f t completely unconstrained. To esta b l i s h q u a l i t a t i v e constraints on the 84 chloride solution model, i t was assumed that non-ideal interactions in the aqueous solution are largely due to the presence of charged species. Accordingly, the chloride solution model was constrained to trend toward i d e a l i t y in the temperature region where the neutral chloride species chl dominate. WQ was forced to be l i n e a r l y temperature chl chl dependent by allowing only WH and Wg to be non-zero. In chl chl addition, WH and Wg were constrained to have the same chl sign, and WG was a r b i t r a r i l y constrained to be 0±1kJ at 1000°C. To allow lnKD for the t a l c - c h l o r i d e equilibrium to tal c remain approximately composition independent, was allowed to be non-zero, but temperature independent. The results of a second MINOS run with these changes in the constraints are l i s t e d in tables II.7 and II.8. This set of parameters w i l l be referred to as Model 2. Calculated * lnKQ curves are compared to the data in figures II.8 through 11.11 and the functions are plotted on figure 11.12. Many of the inconsistencies noted above for Model 1 are absent from Model 2. Unfortunately, the price of th i s improved model-data correspondence is rejection of one of the most convenient basic assumptions about the properties of the aqueous chloride s o l u t i o n . The d e t a i l s are l i s t e d by mineral. Olivine: Model 2 lnKD curves are included within 2a error brackets for the entire o l i v i n e - c h l o r i d e data set. Only a few of the 1a brackets are missed. A review of Model 1 and Table II.7 Endmember thermodynamic properties for Model 2 NAME FORMULA H° H298 s! 0 298 k 0 k , kz k, V (dx10": 1 ) ( J / : "c) ( J / ' C ) (x10"3) (x10-5) (cm : ' ) Fe-Ta1c F e i S i i O i o ( O H ) ; -4790 . 7 365 .00 678 .86 - 11701 -4683 17916 148 . 74 Talc MgiSi «0io(OH)7 -5898. .6 261 .04 664 . 1 1 -2147 -5187 -3274 136 .04 Fayal i te Fe*S10. - 1476 . 8 150 .60 248 .93 0 - 1924 -1391 46 . 12 For s t e r i te Mg2 S i 0 « -2174. .0 94 .21 238 .64 0 -2001 -1 162 43 .60 Ferros i1i te FeSiOs -1193. 2 95 . 25 173 . 74 -946 - 1367 1116 32 .96 enstat i te . MgSi03 - 1545. . 7 66 . 17 166 . 58 -2271 -1201 2792 31 . 34 Fe-Anthophy11i te Fe/Si .0*.(OH) z -9365. 8 934 .12 1316 .31 -24235 -8445 35523 277 .04 Anthophy11i te Mg,S i•0; ;(OH ) , -1207 1. O 535 .20 1219 .31 -347G6 -5767 44009 265 . 63 FeCl* FeCl ? 0. 0 88 . 19 0 .0 0 0 0 34 , . 59 MgCl ! MgCl , -382 . 1 O .0 0 .0 0 0 0 0. ,0 00 cn 86 Table II.8 Model 2 Margules parameters. A l l parameters pertain to 1 mole of Fe+Mg. Talc Olivine Ortho- Antho- Chloride pyroxene p h y l l i t e WH(kJ) -2.830 44.63 7.48 0.575 -10.63 W S ( J / ° C ) 0.0 50.00 1 1 .45 0.0 -7.57 Wv(J/bar) 0.0 0.012 -0.016 0.0 0.0 A (J/°C) 0.0 26.41 -5.905 0.0 0.0 C (xlO'5) 0.0 -710.8 0.0 0.0 0.0 Q (xlO"1 0) 0.0 923.2 0.0 0.0 0.0 Model 2 parameters, and comparison of figures II.7 and 1 1 . 1 2 , shows that t h i s improvement in model-data correspondence i s e n t i r e l y due to the added non-ideality in the chloride solution. Optimization of the o l i v i n e s o l i d solution model continues to s t r a i n against the upper l i m i t of the calorimetric constraints. Orthopyroxene'. Figure II.9 shows very l i t t l e change in model-data correspondence compared to Model 1 . However, comparison of figures II.7 and 1 1 . 1 2 shows that the W ° ^ X model is now separated farther from the W°^" model. This results in improvement of the correspondence between thermodynamic model and the olivine-orthopyroxene ion-exchange data included in the data base (M. Engi, pers. c omm.). 87 J I I I - * i 1 1 1 1 r 0.0 0.2 0.4 0.6 0.8 1.0 X M g (Olivine) * Figure II.8 Comparison of o l i v i n e lnK^ data with curves calculated with Model 2 thermodynamic parameters, (a) A l l 2kb data plus 450°C (1kb) data. 88 Figure II.8 (b) Data at 600°C (1kb and 4kb). 89 -1 -_E - 2 -- 3 -4 A 680°C 2kb A 800°C 2kb 680c 4 v TV 800e 0.0 0.2 0.4 0.6 0.8 X M g (Orthopyroxene) 1.0 Figure II.9 Comparison of orthopyroxene lnKQ data with curves calculated with Model 2 thermodynamic parameters, 90 0 --1 -* a _E - 2 -- 3 --4 0.0 1 600°C 2kb A 650°C 2kb A 700°C 2kb 0.2 0.4 0.6 0.8 X M g (Orthoamphibole) 1.0 Figure 11.10 Comparison of orthoamphibole lnKD data with curves calculated with Model 2 thermodynamic parameters. 91 OH - H * a <= -2-I -4 0.0 A 400°C 2kb A 500°C 2kb 0.2 0.4 0.6 X M g (Talc) 0.8 1.0 Figure 11.11 Comparison of tal c lnK^ data with curves calculated with Model 2 thermodynamic parameters. 92 Figure 11.12 Comparison of the four Model 2 W~ functions. 93 Anthophyllite: Like the W ° ^x model, the orthoamphibole s o l i d solution model has shifted to a lower WQ value. A of ^0.5kJ i s now s u f f i c i e n t to f i t the lnK^ data. The discrepancy between thermodynamic model and natural olivine-anthophyllite and talc-anthophyllite pairs p e r s i s t s . DISCUSSION ENDMEMBER PROPERTIES: Collaborative e f f o r t s are already underway to conclude evaluation of the MgO-Si02-Fe-0-H-C database. The Mg-Fe chloride ion-exchange data w i l l be included, but the 'weight' this data i s given must be adjusted given the uncertainties exposed here. A complete description of the contents of the database, along with the computational results and their petrologic implications, w i l l appear elsewhere. Both the Mg and Fe endmembers of the o l i v i n e and orthopyroxene solutions are constrained by calorimetry and net-transfer phase e q u i l i b r i a . The thermodynamic properties presented here for these endmembers w i l l change very l i t t l e when the role of the data presented here i s reevaluated. The same is true of the Mg-endmembers of the talc and anthophyllite solutions. No experimental constraints exist for the Fe-endmembers of t a l c and anthophyllite. The thermodynamic properties calculated for these two endmembers must be expected to change as more data becomes available for the t a l c , anthophyllite and aqueous Mg-Fe chloride 94 solutions. SOLID SOLUTION MODELS: The ideal-mixing constraint placed upon the chloride solution in Model 1 appears to be inappropriate. The constraints placed upon the chloride solution model in Model 2 are somewhat arb i t r a r y and need to be confirmed or modified by independent data. U n t i l such data are a v a i l a b l e , the only quantities unambiguously established by the chloride ion-exchange experiments are endmember a c t i v i t y r a t i o s : mineral:chloride a c t i v i t y ratios and, where dif f e r e n t minerals have been studied over the same P-T-mT conditions, mineral:mineral a c t i v i t y r a t i o s . Accordingly, any modifications made to the absolute value of the chloride solution properties must also modify the value of s o l i d solution properties constrained by the ion-exchange experiments. In the mean time, some of the features and implications of s o l i d solution properties calculated in the above examples can be discussed. Olivine: The o l i v i n e s o l i d solution model represented by the Model 2 parameters i s firmly sandwiched between two opposing constraints: the calorimetric measurements and the chloride ion-exchange data. The Model 2 o l i v i n e solution w i l l remain the most comprehensive model u n t i l the implied non-ideality in the aqueous solution can be confirmed (or disproved) and q u a n t i f i e d . The most notable feature of t h i s model i s i t s prediction of a W^"*" at low temperature (<800°C) 95 which is s i g n i f i c a n t l y higher than predicted by previous models (e.g. Engi,1980a; Andersen and Lindsley, 1981). Orthopyroxene: The Mg-Fe orthopyroxene s o l i d solution models represented by Model 1 and Model 2 parameters are similar in form, but d i f f e r in d e t a i l . The primary d i s t i n c t i o n between Model 1 and Model 2 i s in the treatment of the chloride phase. Accordingly, the d e t a i l s of the orthopyroxene model, p a r t i c u l a r l y at T<800°C, must remain somewhat tentative u n t i l the properties of the aqueous solution are more thoroughly understood. In the mean time, the Model 2 parameters must be chosen as most appropriate for the orthopyroxene s o l i d solution based upon the more favorable model-data correspondence of Model 2. The available data constraining the properties of Mg-Fe orthopyroxenes includes measurements of the i n t r a c r y s t a l l i n e exchange of Mg and Fe between the M1 and M2 octahedral s i t e s . A previous analysis of orthopyroxene bulk properties based upon the i n t r a c r y s t a l l i n e exchange alone (Navrotsky, 1971) i s consistent with the Model 2 orthopyroxene only at high temperatures. (Navrotsky's calculated values of GE X correspond to W°p x= - 4 3 0 0 J at 500°C and -2440J at 1250°C) In Appendix G i t i s shown that a detailed 'microscopic' solution model can be simultaneously consistent with the i n t r a c r y s t a l l i n e ion-exchange data and with the bulk s o l i d solution properties predicted by the Model 2 parameters over the temperature range in which Model 2 is constrained by data. The d e t a i l s of this microscopic model imply that the 96 observed bulk properties of the orthopyroxene s o l i d solution are the summation of two opposing energies: a negative free energy produced by ordering of Mg and Fe and a positive ' l a t t i c e s t r a i n ' energy resultant from mixing ions of unequal size in a continuous structure. (The Model 2 o l i v i n e is an apt example of a s o l i d solution dominated by thi s second effec t . ) In addition, the microscopic model predicts that the orthopyroxene bulk GE X w i l l r i s e with f a l l i n g temperature only u n t i l about 550°C. At lower temperatures the negative free energy contribution of s i t e ordering becomes the dominant e f f e c t . Both the macroscopic model used in the database calculations and the microscopic model used in Appendix G are formulations symmetric about X°^x=0.5. The chloride-orthopyroxene data-do not require an asymmetric solution model, but these data only cover 2/3 of the possible range in X°PX. Saxena and Ghose(l97l) noted that their Mossbauer spectroscopic measurements of Mg-Fe s i t e ordering were asymmetric with respect to X ° ^x. In Appendix G i t i s shown that the uncertainties inherent in the Mossbauer data tend to drown out thi s asymmetry. However, i t i s quite possible that future research w i l l confirm that the Mg-Fe orthopyroxene solution must be modelled as asymmetric with respect to XM g. Ant hophylIi t e: Models 1 and 2 both assign a small positi v e WG to the anthophyllite s o l i d s o l u t i o n . Due to the narrow temperature range of the chloride ion-exchange data and the 97 remaining uncertainties in the role of the aqueous solution, i t i s inappropriate at th i s time to calculate a temperature dependence for Wgnt^. Once again, the success of Model 2 r e l a t i v e to Model 1 indicates that the Model 2 W^nth i s the better.estimate. As with the orthopyroxene, Mg-Fe ordering has been detected in anthophyllites (e.g. Finger, 1970). The i n t r a c r y s t a l l i n e Mg-Fe ion-exchange has been measured as a function of temperature and time (Seifert and Virgo, 1974, 1975; S e i f e r t , 1977, 1978). There appears to be l i t t l e or no ordering amongst the M1, M2, and M3 s i t e s , but the preference of Fe2 + for M4 is even stronger than the preference for M2 in orthopyroxene (compare Saxena and Ghose, 1971 and S e i f e r t , 1978). Formulation of a 'microscopic' anthophyllite solution model i s not attempted here because the number of site-configurations to be considered i s large and the available i n t r a c r y s t a l l i n e ion-exchange data covers only a narrow composition range. However, the insight gained from applying such a model to the orthopyroxene solution allows us to q u a l i t a t i v e l y predict the c h a r a c t e r i s t i c s of the anthophyllite s o l i d s o l u t i o n . Although Fe2 + fractionation in anthophyllite i s somewhat stronger than that in orthopyroxene, Fe2 + i s fractionated into only 2 of 7 si t e s (per formula u n i t ) . Therefore the contribution of s i t e ordering to the bulk s o l i d solution properties i s expected to be subdued compared to i t s effect in the the 98 orthopyroxene s o l u t i o n . If the contribution of l a t t i c e s t r a i n energy i s similar for these two chain s i l i c a t e s , the bulk W^nt^ may be predicted to be somewhat higher than W ° ^x The Model 2 W^"1"*1 i s q u a l i t a t i v e l y consistent with these considerations. Talc: The t a l c - c h l o r i d e ion-exchange data i s of l i t t l e use in defining t a l c s o l i d solution properties while the properties of the aqueous solution remain uncertain. The t a l c data are not even of much use for estimating properties by comparison with the other minerals studied here. This is because the ta l c data were co l l e c t e d under P-T conditions at and beyond the P-T l i m i t s of the other data sets. (The only overlap is with three o l i v i n e half-brackets at 450°C, 2kb) In addition, the ta l c data-set is characterized by r e l a t i v e l y wide compositional brackets and r e l a t i v e l y high uncertainty in ta l c f i n a l compositions. More research i s required before the talc s o l i d solution properties can be constrained by ion-exchange experiments with aqueous chlor ides. In the meantime, i t may be f r u i t f u l to compare tal c parameters from Model 1 and Model 2 with estimates inferred from the example set by the microscopic orthopyroxene solution model. Mossbauer spectroscopy has f a i l e d to detect Fe-Mg ordering in natural t a l c s (Blaauw et a l , 1980). Qualitative comparison with the orthopyroxene model would therefore predict that the t a l c s o l i d solution is dominated by the positive 99 gx contributed by ' l a t t i c e s t r a i n ' . Model 1 and Model 2 talc values for WQ (0 and -2.8kJ respectively) are not consistent with th i s argument. Un t i l more dependable constraints are a v a i l a b l e , the Fe-Mg t a l c solution may be best modelled as i d e a l . CONCLUSIONS The use of aqueous chlorides as a solution phase offers d i s t i n c t p r a c t i c a l advantages when performing ion-exchange experiments with s o l i d solution phases. However, i t appears that thermodynamic interpretation of such experiments i s not at a l l straightforward. The Mg-Fe ion-exchange data presented here show that the contribution of the aqueous chlorides to KD i s dependent on the t o t a l chloride concentration. Thermodynamic analysis of the data indicates that the contribution of the aqueous chlorides may also be composition dependent. U n t i l the role of the aqueous solution i s more quantitatively established, such ion-exchange experiments are of l i t t l e use in characterizing a single s o l i d solution phase. For the moment, the primary u t i l i t y of aqueous chlorides i s as a medium through which mineral properties can be compared. The implications of uncertainties in the chloride solution properties on the calculated solution properties of minerals studied here are discussed above. The implications these uncertainties have on previously published chloride 100 ion-exchange studies must also be addressed. Previous chloride-ion-exchange studies have put l i t t l e or no ef f o r t into characterizing the aqueous solution and i t s role in the experimental r e s u l t s . In l i g h t of the data analysis presented here, s o l i d solution properties calculated from these previous studies must be.considered suspect u n t i l the properties of each pertinent aqueous mixture of chlorides have been examined. The questions that need to be addressed by future research with aqueous Mg-Fe chlorides include: What is the dependence of KQ on mT at 450°C (1kb and 2kb) where only half brackets are established here? What i s the dependence of KD on mT at T > 600°C? What i s the magnitude of the chl implied dependence of KD on ? What is the cause of t h i s compositional dependence? What are the i d e n t i t i e s of a l l aqueous species which s i g n i f i c a n t l y contribute to the measured d i s t r i b u t i o n c o e f f i c i e n t ? The above analysis of the o l i v i n e , orthopyroxene, ta l c and anthophyllite s o l i d solutions suggests mineralogical questions to be answered by future research: Are the orthopyroxene solution properties asymmetric with respect to X5! |LX? What are the energetic and crystallographic differences between synthetic and natural anthophyllite? What are the properties of the ta l c solution? What is the relationship between tal c and minnesotaite? 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MIX COMPONENTS: S i 02: S i l i c i c acid (H2Si03'nH20; Fisher reagent grade, lot 730944) was heated to =400°C for a few minutes to drive off the bulk of the H20 ad then heated at 1200°C for 12 hours. The resulting s o l i d , but f r i a b l e mass of f i n e l y c r y s t a l l i n e a - c r i s t o b a l i t e was broken up, ground under alcohol for 2 hours to reduce grain s i z e , and then dried at 1000°C for 2 hours. MgO: Fisher A.C.S. grade MgO (lot 741694) was heated at 1300°C for 24 hours to dry and also to increase grain size (this reduces material loss due to a i r currents during the weighing process). 1 15 1 16 Fe203: Fisher reagent grade ferric-oxide (lot 725030) was heated at 900°C for 10 hours to dry and to increase grain s i z e . Fe: Johnson, Matthey and Co. iron sponge (lot S7294) was stored in a dessicator for more than 2 months prior to use. The oxygen content of a representative sample of thi s iron sponge was determined with the method of Turnock et a l ( l 9 7 3 ) . From the measured value of 2.45 wt.% 02, the equivalent FeO content was calculated to be 11.0 wt.%. MIX CALCULATIONS'. For each mix the required weights of S i 02, MgO and FeO were calculated such that the t o t a l mix weight was 3.0g. The weights of Fe203 and iron sponge required to produce 1.0g of stoichiometric FeO were calculated and then multiplied by the FeO weight required for each mix. Each mix component was weighed separately into a p l a s t i c weighing boat and washed with alcohol into an agate mortar. HOMOGENIZATION: The homogenization process began with hand grinding; both under alcohol (reagent grade; 95% ethanol, 5% H20) and dry for about 10 minutes each. Hand grinding i s tedious, but much more e f f e c t i v e than an automatic mortar in breaking up the larger lumps of material. The hand grinding was followed 1 17 by grinding under alcohol in an automatic mortar for =0 hour. This was followed by a few more minutes of dry hand grinding to mix in portions of the mix which had dried onto the pestle and high on the sides of the mortar during automatic grinding. Grinding Fe-bearing mixes in the automatic mortar quickly revealed that small amounts of the Fe metal tended to adhere to the surface of the mortar. This threat to maintaining the mixes on composition was negated, or at least minimized, by 'pre-treating' the surface of the mortar. This pre-treatment consisted of grinding a portion of an iron bearing mix of similar composition in the automatic mortar and then washing out the mortar. The amount of Fe thus l e f t adhered to the mortar surface should be close to a 'steady state' amount for that mix. The mixes used for pre-treatment were early (unuseable) mixes which had suffered iron loss during grinding. 118 APPENDIX B: AQUEOUS ANALYSES QUENCH PH: Quench pH of the run f l u i d could be measured for cases in which the run f l u i d could be separated from the capsule and i t s c r y s t a l l i n e contents by ce n t r i f u g i n g . The pH measurement was made using a micro-combination pH electrode (Microelectrodes, Inc., Londonderry, N.H., U.S.A.) which requires as l i t t l e as 5M1 collected in the conical bottom of the centrifuge v i a l (Pearce React i vial). Early quench pH measurements exhibited a continuous d r i f t which was interpreted to be the result of chemical reaction of atmospheric a i r with the run f l u i d . To prevent such reactions from occuring prior to and during the pH measurement, capsule centrifuging was conducted with the centrifuge v i a l flushed with argon, and the pH measurement was made with the open volume immediately surrounding the electrode flushed with argon. Quench pH measurements made with these precautions were free of d r i f t . Table B1 l i s t s the quench pH measurements, a l l of which are from o l i v i n e ion-exchange experiments. 1 19 Table B1. Quench pH measurements. Run# pH Run# pH 64 5.64 129 5.85 66 5.44 1 30 4.80 67 5.39 1 33 5.73 68 4.97 134 5.78 69 5.10 1 35 5.67 70 5.12 1 36 4.74 71 5.18 142 4.74 101 5.53 145 4.67 1 02 4.88 1 46 5.45 1 03 4.89 147 4.59 1 16 5.49 1 63 5.32 1 17 4.97 1 64 5.93 121 5.53 1 65 5.18 1 22 5.35 166 5.78 1 28 5.42 169 3.86 ATOMIC ABSORPTION SPECTROPHOTOMETRY: Analysis of aqueous Fe and Mg was performed on a Varian Techtron model AA4 spectrophotometer using an air-acetelene flame. Spectral l i n e s at 2852A and 2483A were used for Mg and Fe respectively. The standard concentrations and sample d i l u t i o n s used were designed to r e s t r i c t absorbance levels to the 0.1 to 0.4 range. A series of 3 standards, which span the concentration range of the 'unknown' samples, was 1 20 measured once before and once after each group (5 to 10) of samples was measured. Each sample group was measured 3 to 5 times (depending on available solution volumes) with each group measurement separated by a single measurement of the standard s e r i e s . The absorbance meter was zeroed while aspirating a 'blank' (a sample of the a c i d i f i e d water used in a l l d i l u t i o n s ) before every absorbance reading. Sample concentrations were calculated separately for each sample group by means of a c a l i b r a t i o n function which was produced by least squares f i t t i n g to the six standard absorbances (3 leading and 3 t r a i l i n g ) associated with that group. The ca l i b r a t i o n function used i s a quadratic in absorbance which is constrained to pass through zero concentration at zero absorbance. Adding together the standard error of repl i c a t e measurements, estimated accuracy of standards and estimated accuracy of d i l u t i o n s indicates that, in general, Mg concentrations are accurate to ±3% and Fe concentrations are accurate to ±3.5%. Standards : Atomic absorption standards were made by c a r e f u l l y weighing d r i e d , reagent grade MgO and Fe203 into volumetric flasks containing d i s t i l l e d water and s u f f i c i e n t reagent grade HC1 to dissolve the oxide. Primary standards were made in this manner at concentrations of lOO^g MgO per ml and 500Mg Pe203 per ml. Secondary standards were made by d i l u t i n g the primary standards with the same a c i d i f i e d 121 d i s t i l l e d water used to di l u t e the experimental run f l u i d s . The secondary standard selection judged optimal was 1, 2, 4 and 6ngMgO/ml and 20, 40, 60 and 80MgFe203/ml. Dilution of Run Fluids: A l l d i l u t i o n s were made using a c i d i f i e d d i s t i l l e d H20 to s t a b i l i z e the s o l u b i l i t y of ionic Fe and Mg. The a c i d i f i e d water consisted of 2ml of reagent grade HN03 in each l i t e r of d i s t i l l e d water (0.03m in HN03). N i t r i c acid was chosen over HCl to allow measurement of the chlorine concentration in the (diluted) run f l u i d . I n i t i a l d i l u t i o n volumes were chosen to produce solutions containing approximately 0.005 moles t o t a l Fe+Mg. This results in convenient volumes of solution containing s u f f i c i e n t concentrations of Fe and Mg for atomic absorption; even at the extremes of Fe-Mg compositon range. This concentration l e v e l i s also in the range appropriate for chlorine a n a l y s i s . For 2m run f l u i d s , 25/ul was t y p i c a l l y extracted and added to 10ml of a c i d i f i e d water resulting in an i n i t i a l d i l u t i o n factor of 400. The secondary d i l u t i o n factors appropriate to f a c i l i t a t e atomic absorption analysis were generally calculable since the approximate proportions of Fe and Mg in the run f l u i d could be predicted based on the work of Schulien et a l ( l 9 7 0 ) . Secondary d i l u t i o n factors were generally between 1 and 10 for Fe and between 5 and 50 for Mg. 1 22 CHLORINE ANALYSIS: Aqueous chlorine concentrations were measured with a Buchler Cotlove Chloridometer (Buchler Instruments, Inc., Fort Lee, N.J., U.S.A.). The instrument measures the time required for complete coulometric t i t r a t i o n of CI" in an aliquot of solution (see Cotlove et a l , 1958). Concentrations are determined by comparison with standards and normalizing from the actual aliquot volume to l l i t e r . Any non-linearity of the dependence of t i t r a t i o n time on t o t a l CI" was avoided by adjusting aliquot volumes so that every t i t r a t i o n took approximately the same time (^60 seconds). T i t r a t i o n of standards indicated that there was no s i g n i f i c a n t dependence of t i t r a t i o n time on aliquot volume (keeping t o t a l CI" in the aliquot constant) for aliquot volumes in the 50 to 200jul range. For routine operation, sample d i l u t i o n s were designed to produce solutions containing approximately Ijtxmole CI" in a 100M1 a l i q u o t . S t a t i s t i c a l analysis of re p l i c a t e measurements indicates that the chlorine analyses are accurate to ±6% of the amount present. 1 23 APPENDIX C: ELECTRON MICROPROBE ANALYSES The main features of the standard analysis and p a r t i c l e analysis techniques and d e t a i l s of their respective sample mounting techniques are l i s t e d below followed by a summary of a l l microprobe analyses (table C1). The crystal-face analysis technique i s not discussed separately: Its mounting technique i s that of the p a r t i c l e analyses and i t s analysis procedure i s that of the standard analyses. STANDARD ANALYSIS: Sample Mounting: Mineral grains were mounted in 1 inch disks of fused Buehler Transoptic: a clear p l a s t i c powder with a 20 to lOOMm grain s i z e . Blank disks of pure Transoptic are f i r s t fused at =150°C under a 4200psi pressure in a 1 inch c y l i n d r i c a l mold. Six shallow (2mm) holes are d r i l l e d into one surface of each blank. Each hole is packed with a homogenized mixture of Transoptic powder (=*70%) and mineral grains. The mount i s then returned to the c y l i n d r i c a l mold and re-pressed at the same P and T. To obtain a f l a t polish across each mineral grain (in spite of the hardness contrast between the grain and Transoptic), coarse grinding and a l l but the f i n a l polishing stage i s performed with diamond abrasives on metal laps. The f i n a l polishing stage consists of wet polishing on a cl o t h 124 covered lap with Li nde B alumina for a few seconds,. Microprobe Analysis'. (ARL-SEMQ and ARL-EMX) Accelerating potential Emission current Objective aperture Specimen current Beam diameter Counting time Standards Data reduction PARTICLE ANALYSIS'. Sample Mounting: Mineral grains were deposited on a polished graphite substrate from an alcohol suspension. A l l p a r t i c l e mounts were carbon coated prior to a n a l y s i s . The graphite stubs used as a substrate for p a r t i c l e analysis were cut from l/4inch diameter high purity spectroscopic electrode rods. The stubs of graphite rod were mounted via set-screws into 1inch diameter steel holders (5 1 5kV 1 50MA 1 OOMm 1 5nA -3 Mm 20 seconds 30 to lOOum synthetic f o r s t e r i t e , synthetic f a y a l i t e and synthetic enstatite grains; mounted as above. Bence-Albee 125 stubs per holder) which f i t d i r e c t l y into the microprobe specimen stage. While mounted in the steel holder, the stubs were polished f l a t by dry grinding on a series of abrasive glass plates. The abrasive surface of each glass plate had been l i g h t l y ground with a d i f f e r e n t grade of s i l i c o n carbide or aluminum oxide abrasive powder. Microprobe Analysis: (ARL-SEMQ) Accelerating potential Emission current Objective aperture Specimen current Beam diameter Counting time Standards Data reduction 1 5kV 1 50uA 40 Mm 35nA 10MHI square raster 100 seconds same as those used for standard analysis Bence-Albee plus an empirical graphical correction The empirical correction curve was formulated in terms of since t h i s was the desired product of the analyses. The correction curve was cal i b r a t e d by analyzing a series of fine-grained synthetic o l i v i n e s . The correction curve used is i l l u s t r a t e d in figure C 1 . 126 X 0 .04 0.0 0.2 0.4 0.6 0.8 1.0 Apparent XMg Figure CI. Empirical c a l i b r a t i o n curve for p a r t i c l e analysis c o r r e c t i o n . The 1a error boxes surround the standard o l i v i n e analyses which were used to define the curve. Table CI. Summary of microprobe analyses. The more cryptic column headings are: PH=phase, M=method. The abreviations are OL=olivine, OP=orthopyroxene, OA= orthoamphibole, S=standard analysis, P=particle a n a l y s i s , F=crystal face a n a l y s i s . The formula cations are based upon 4 oxygens for o l i v i n e , 6 for orthopyroxene, and 23 for orthoamphibole. For the p a r t i c l e analyses, only XM g has been corrected via the empirical c a l i b r a t i o n (figure C1). The last column indicates the number of analyses averaged in cal c u l a t i n g the l i s t e d values. WT% Formula Cations RUN PH M TOTAL Mg Fe Si X (1a) # 1 42 OL S 1 42 OL P 1 43 OL S 1 43 OL P 145 OL S 1 45 OL p 1 46 OL s 146 OL p 1 47 OL P 163 OL s 1 63 OL p 164 OL p 1 65 OL s 165 OL p 166 OL s 166 OL p 167 OL s 167 OL p 1 1 6 OL s 1 1 6 OL p 1 1 7 OL s 121 OL s 91.60 0.744 20.45 0.646 96.74 0.804 20.96 0.864 99.81 0.207 20.86 0.308 96.73 1.390 12.58 1.298 21.83 1.945 98.75 0.211 24.41 0.140 19.77 0.722 97.99 0.764 23.53 0.662 97.90 0.766 16.75 0.642 00.11 0.647 18.55 "0.793 99.45 0.984 11.93 0.927 99.82 0.984 00.07 0.996 1 .235 1 .010 1 .363 0 .995 1 .174 1 .011 1 . 1 47 0 .995 1 .781 1 .006 1 .697 0 .998 0 .599 1 .010 0 .549 1 .076 0 .036 1 .010 1 .786 1 .002 1 .895 0 .983 1 .228 1 .000 1 .227 1 .005 1 .416 0 .961 1 .223 1 .006 1 .367 0 .996 1 .345 1 .004 1 .240 0 .984 0 .999 1 .008 1 .045 1 .014 1 .004 1 .006 1 .006 0 .999 0. 376( 13) 6 0. 338( 19) 1 3 0. 407( 18) 6 0. 455( 14) 1 1 0. 1 04( 3) 7 0. 1 63( 7) 6 0. 702( 8) 7 0. 728( 4) 5 0. 984( 10) 13 0. 1 06( 4) 3 0. 074( 11) 12 0. 4 1 9 ( 8) 15 0. 384( 11) 7 0. 334< 8) 16 0. 385( 12) 4 0. 347) 1 1 ) 18 0. 325< 5) 5 0. 388< 14) 1 4 0. 496 ( 5) 7 0. 493< 4) 10 0. 495< 5) 7 0. 498( 3) 8 128 WT% Formula Cations RUN PH M TOTAL Mg Fe Si Mg (1a) # 121 OL P 17.54 0.906 1 .083 1 .006 0.478 (10) 9 122 OL S 100.26 0.997 1 .009 0.997 0.497 ( 3) 8 122 OL P 21.31 1 .005 0.985 1 .005 0.529 (20) 1 0 124 OL P 10.40 1 .548 0.427 1.012 0.807 ( 9) 1 6 1 35 OL S 97.81 1 .043 0.953 1 .002 0.522 (24) 5 1 35 OL P 20.81 1.111 0.888 1 .000 0.582 (21 ) 1 0 1 36 OL s 97.39 0.983 1 .005 1 .005 0.494 ( 4) 8 1 36 OL P 20. 12 0.894 1 .092 1 .007 0.472 ( 15) 1 0 1 99 OL s 100.40 0. 196 1 .791 1 .007 0.098 ( 5) 8 199 OL P 30.43 0.239 1 .824 0.968 0. 1 23 (20) 7 200 OL s 99.87 0.556 1 . 436 1 .004 0.279 (20) 7 200 OL P 1 4. 96 0.627 1 .391 0.990 0.327 (23) 1 0 25 OL s 99.66 0.203 1 .778 1 .009 0. 1 02 ( 4) 8 26 OL s 99.18 • 0.558 1 .422 1.010 0.282 (14) 8 26 OL p 21.17 0.575 1 .427 0.999 0.299 (19) 22 27 OL s 99. 18 0.527 1 .462 1 .005 0.265 (18) 8 27 OL p 20.86 0. 521 1 .505 0.987 0.270 (18) 1 3 37 OL s 99.55 1 . 180 0.800 1 .010 0.596 ( 4) 8 37 OL p 15.17 1 . 142 0.823 1.018 0.607 (12) 1 3 38 OL s 98.98 1 .374 0.596 1.015 0.698 ( 5) 8 38 OL p 1 6.42 1 .290 0.690 1 .010 0.679 (13) 12 39 OL s 99.42 1 .486 0.486 1.014 0.754 ( 6) 5 39 OL p 10.50 1 .458 0.500 1 .021 0.770 ( 8) 1 2 40 OL p 5.30 1 .528 0.462 1 .005 0.792 (11) 1 7 41 OL s 98.70 1 .800 0. 192 1 .004 0.904 ( 3) 6 41 OL p 3.80 1 .660 0.269 1 .035 0.882 ( 9) 8 41 OL F 86.20 1 .755 0.233 1 .006 0.883 ( 9.) 7 42 OL s 99.46 1.916 0.081 1 .002 0.960 (14) 6 42 OL p 7.93 1 .745 0.223 1.016 0.909 (10) 1 6 43 OL s 99.56 0.985 1.011 1 .002 0.494 ( 2) 8 43 OL p 17.27 0.880 1 . 1 07 1 .007 0.465 ( 9) 1 3 64 OL s 100.17 1 .980 0.016 1 .002 0.992 ( 1 ) 8 129 WT% Formula Cations RUN PH M TOTAL Mg Fe Si Mg (1a) # 66 OL S 98.08 0.976 1 .000 1.012 0.494 ( 2) 8 67 OL P 15.56 0.954 1 .050 0.998 0.500 ( 5) 1 3 68 OL S 99.46 0.999 0.988 1 .006 0.503 ( 8) 7 1 19 OL s 100.04 0.995 1 .005 1 .000 0.497 ( 3) 8 1 19 OL p 1 9.44 0.999 0.963 1 .019 0.533 (10) 1 2 133 OL s 99.51 0.991 1 .007 1 .001 0.496 ( 1 ) 2 1 33 OL p 20.31 0.885 1 . 1 24 0.996 0.463 (11) 10 134 OL s 100.09 0.985 0.999 1 .008 0.497 ( 2) 7 101 OL s 99.48 0.986 1 .002 1 .006 0.496 ( 3) 8 101 OL p 18.26 0.891 1 .081 1.014 0.474 (15) 1 3 102 OL s 99.10 0.986 1 .003 1 .005 0.495 ( 4) 7 1 02 OL p 20.22 0.946 1 .027 1.013 0.503 ( 8) 1 2 1 03 OL s 98.74 0.982 1 .000 1 .009 0.496 ( 4) 7 103 OL p 1 6. 44 0.883 1 .081 1.018 0.472 ( 6) 1 2 128 OL p 16.30 0.990 1.010 1 .000 0.519 (23) 10 129 OL s 100.41 0.990 1 .009 1 .001 0.495 ( 3) 7 129 OL p 17.85 0.883 1.110 1 .004 0.465 (12) 10 130 OL s 100.54 0.989 1 .004 1 .004 0.496 ( 5) 6 130 OL p 17.61 0.883 1 .091 1.013 0.469 ( 8) 10 174 OL p 6.88 1 .645 0.324 1.016 0.855 ( 9) 1 1 197 OL s 100.12 0. 1 96 1 .790 1 .007 0.099 ( 7) 6 197 OL p 24.71 0. 1 47 1 .865 0.994 0.078 ( 6) 1 1 225 OL p 25.30 0.257 1 .794 0.974 0. 1 30 (14) 16 226 OL p 24.21 0.537 1 .504 0.979 0.270 (12) 26 227 OL p 1 6.84 1 .595 0.399 1 .003 0.820 (12) 19 69 OL s 99.90 0.208 1 .780 1 .006 0. 1 05 ( 2) 8 70 OL s 99.25 0.214 1 .780 1 .003 0. 1 07 ( 1 ) 8 71 OL s 99.23 0.844 1 . 150 1 .064 0.423 ( 4) 6 72 OL s 99.38 1 .621 0.378 1 .001 0.811 ( 2) 8 21 1 OL s 99.05 1 .598 0.403 1 .000 0.799 ( 5) 8 21 1 OL p 9.98 1 .486 0.482 1.016 0.780 ( 3) 6 212 OL s 98.38 1 . 1 94 0.786 1.010 0.603 (14) 6 1 30 WT% Formula Cations RUN PH M TOTAL Mg Fe Si Mg (1a) # 212 OL P 1 4.40 1 . 188 0.800 1 .006 0.623 ( 7) 12 213 OL s 98.36 0.787 1 .204 1 .005 0.395 ( 4) 6 21 3 OL P 1 7.70 0.753 1 .264 0.991 0.392 ( 6) 9 75 OL s 99.44 0.209 1 .782 1 .004 0. 1 05 ( 2) 7 169 OL s 99.94 1.721 0.270 1 .005 0.865 ( 1 ) 8 169 OL P 24.58 1 .6.50 0.293 1 .028 0.868 ( 2) 2 169 OL F 96.29 1 .790 0.251 0.979 0.877 ( 4) 3 1 70 OL s 100.09 1 .623 0.386 0.995 0.808 ( 6) 7 170 OL F 97.62 1 .641 0.349 1 .005 0.825 ( 7) 7 202 OL. S 99.25 0.228 1.759 1 .007 0.115 ( 5) 8 202 OL P 22.47 0.214 1 .798 0.994 0.113 (12) 7 203 OL s 100. 10 0.843 1 . 148 1 .004 0.420 (12) 7 204 OL s 100.97 1.517 0.461 1 .005 0.768 (20) 5 204 OL p 16.53 1 .427 0.557 1 .008 0.745 (12) 9 264 OP s 98.65 0.730 1 .251 2.009 0.369 (41 ) 8 264 OP p 21 .95 0.644 1.316 2.019 0.345 (26) 9 265 OP s 98.87 0.790 1 . 194 2.008 0.398 (16) 6 265 OP p 14.76 1 .086 0.920 1 .996 0.567 (16) 8 266 OP s 97.98 1 . 140 0.839 2.011 0.576 (20) 6 266 OP p 1 5.88 1 .232 0.628 2.069 0.689 (17) 10 267 OP s 98.31 1 .525 0.460 2.007 0.768 (41 ) 6 267 OP p 22.20 1 .406 0.568 2.013 0.738 (22) 9 268 OP s 99.26 1 .642 0.362 1 .998 0.819 (43) 7 268 OP p 21 .74 1 .671 0.253 2.038 0.886 (25) 7 269 OP p 18.05 1 .821 0. 1 43 2.018 0.937 ( 9) 8 277 OP s 99.08 0.721 1 .268 2.005 0.363 (20) 5 277 OP p 16.90 0.774 1 .261 1 .982 0.400 (17) 9 278 OP s 98.72 1 .582 0.397 2.011 0.799 (19) 9 278 OP p 16.13 1 .562 0.402 2.018 0.818 (11) 8 279 OP s 98.08 1 .891 0. 100 2.005 0.950 (55) 5 279 OP p 18.32 1 .739 0.236 2.013 0.896 (16) 10 228 OP s 98.89 0.851 1 . 134 2.008 0.429 (45) 10 131 WT% Formula Cations RUN PH M TOTAL Mg Fe Si XMg { ] o ) # 228 OP P 27.77 0.831 1 .068 2.050 0.458I 15) 6 228 OP F 100.41 0.899 1 .001 2.050 0.466I 9) 6 229 OP S 98. 16 1 .035 0.953 2.006 0.520< 42) 1 0 229 OP P 16.45 0.982 0.975 2.022 0.526 17) 7 229 OP F 99.65 1 .027 0.923 2.025 0.527 (11) 8 230 OP S 99.09 1 .398 0.590 2.007 0.703 (62) 9 230 OP P 15.73 1 .365 0.520 2.058 0.750 (14) 8 230 OP F 99.35 1 .485 0.498 2.008 0.749 (16) 4 231 OP S 97.81 1.611 0.407 1 .991 0.798 (17) 7 231 OP P 1 6.70 1 .454 0.451 2.047 0.788 ( 7) 6 2 32 OP s 97.79 1 .736 0.289 1 .988 0.857 (39) 8 232 OP p 17.90 1 .568 0.265 2.083 0.874 (15) 10 233 OP s 98. 16 1 .930 0.051 2.010 0.974 (16) 9 233 OP p 16.21 1 .727 0.083 2.095 0.966 ( 5) 7 304 OA p 6.31 0.843 6.961 7.598 0.114 (12) 8 215 OA p 15.12 2.362 4.958 7.840 0.340 ( 7) 7 188 OA p 1 1 .09 3.585 3.998 7.709 0.496 (21 ) 10 218 OA p 13.90 4.823 2.351 7.713 0.699 (54) 9 300 OA p 12.84 5.940 0.890 8.085 0.887 (34) 10 252 OA p 5.56 2.532 5.294 7.587 0.341 (14) 10 253 OA p 4.28 3.675 4.088 7.618 0.497 (27) 9 283 OA p 5.84 2.654 5.239 7.553 0.354 (13) 10 284 OA p 8.08 3.432 4. 179 7.694 0.473 (18) 10 285 OA p 8.11 4.860 2.560 7.790 0.682 (28) 9 307 OA p 8.66 5.965 0.977 8.029 0.879 (58) 10 308 OA p 5.50 6. 1 25 0.637 8.119 0.919 (38) 9 309 OA p 5.13 2.888 4.824 7.644 0.394 (16) 10 310 OA p 4.39 0.940 7.151 7.455 0. 122 (17) 10 1 32 APPENDIX D: HIGH ACCURACY POWDER XRD The high accuracy XRD peak position measurements required for unit c e l l refinements, c a l i b r a t i o n of peak position as a function of composition, and measurement of mineral composition (based on such a ca l i b r a t i o n ) were performed on a P h i l i p s PW1710 Automatic Powder DiffTactometer. This unit employs a stepping-motor driven goniometer and, i s microcomputer c o n t r o l l e d . Accordingly, automatic, d i g i t a l peak-seeking procedures were used instead of analog, chart-recording methods. A l l measurements were made using Ni f i l t e r e d Cu r a d i a t i o n . A graphite monochromator reduced Fe fluorescence problems to a minimum. PEAK POSITION MEASUREMENT: The strategy chosen for peak measurement with the PW1710 i s one of establishing the 26 position having the absolute maximum intensity for each peak, at low angles rf-spacings are calculated using the Ka, wavelength. For sharp peaks the d i g i t a l peak-seeking procedures can resolve and measure Ka, and Ka2 peaks at angles as low as 4O°20. The effects of counting s t a t i s t i c s are minimized by using longish (10 second) counting times. The precision of each peak position measurement is established through r e p e t i t i o n s . Although the peak measurement procedure i s subsequently time consuming (6 to 12 minutes or more depending on d e t a i l s of the procedure), the entire process 133 for a number of peaks measured for a c e l l refinement can s t i l l be faster than t y p i c a l analog instrument procedures. If the approximate position of the target peaks i s already known, a control program, s p e c i f i c to the mineral, can be written specifying these p o s i t i o n s . This avoids investment of time in measuring the continuum between peaks. In programming the above strategy I made use of two peak-seeking functions provided by P h i l i p s and one programmed by myself. The two delivered with the machine are: MAX: §steps, stepsize, count lime and goniometer position are user-specified. MAX counts x-ray pulses for count time seconds at each of %steps-2+] p o s i t i o n s , each stepsize apart, starting at a position #5t eps•stepsi ze below the position of the goniometer when MAX i s invoked. The position with the maximum x-ray intensity is printed out and the goniometer i s returned to that p o s i t i o n . Some smoothing of counting s t a t i s t i c s i s accomplished by summing the intensity for each position with the i n t e n s i t i e s of on adjacent position on either side, and comparing i n t e n s i t i e s based on these sums. CSP: This i s a continuous scanning routine with peak i d e n t i f i c a t i o n and measurement procedures b u i l t i n . The user spe c i f i e s a scanrate, a counttime and the 29 distance to scan over. The 26 stepsize which separates d i g i t a l intensity measurements is scanrate•countt ime. For each peak i d e n t i f i e d by CSP, the five i n t e n s i t i e s at positions closest to the peak maximum are f i t t e d to a parabola, from which the absolute maximum position i s 134 calculated. The need for a t h i r d routine i s a result of the i n a b i l i t y of the above routines to handle low intensity and broad peaks. CSP i s very precise for strong, sharp peaks. However, the peak-identification part of the routine, over which the user has no c o n t r o l , often misses broad,weak peaks when using a small slepsize. Although MAX always returns a measurement, i t is only as precise as the stepsize being used. In p r i n c i p l e then, MAX can be precise to ±0.005°,. the minimum step size of the goniometer. In pr a c t i c e , counting s t a t i s t i c s confuse the position of the peak maximum over a 26 distance of about 0.02° and MAX only samples 0.01° swaths (at the 0.005° stepsize). The optimum user-programmed routine to circumvent the problems inherent in MAX and CSP would probably be a curve f i t t i n g routine similar to CSP. However, the programming capacity of the PW1710 (operating in an Assembler hybrid) makes programming of such a routine complicated and memory-expensive. I chose instead to write a routine which is very similar to MAX, which I w i l l refer to as MAX9. MAX9 has no variables since variables are not a feature of the PW1710 control language. MAX9 uses a 10 second counting time and the minimum stepsize. It assumes that the starting goniometer position is close to the peak maximum and measures i n t e n s i t i e s at each of 8 steps on either side of the s t a r t i n g position (and also at the starting position i t s e l f ) . Like MAX, comparison of i n t e n s i t i e s i s made based 135 on sums of i n t e n s i t i e s symmetric about the position in question. MAX9, however, uses sums of 9 i n t e n s i t i e s . This means that MAX9 sums over 0.04° swaths, but i t has a precision of 0 . 0 0 5 ° . For single peak measurements, neither CSP nor MAX9 were used alone. If error due to specimen height and the effect of s o l i d solution on mineral c e l l parameters are considered, i t i s clear that, in general, the goniometer position of a part i c u l a r XRD peak cannot be predicted to closer than ±O.25°20! An optimum, high precision set up for CSP was found to be: 0.002°/s scanrate; 10s counttime; 0.02° t o t a l scan range. MAX9, as written, has an e f f e c t i v e range of only O.O4°20. To ensure that the goniometer i s within the range of these two routines successive invocations of MAX with coarser stepsizes and 4 to 5 second count times were used. Although CSP proved to be (potentially) more precise than MAX9, the two procedures were not mixed when measuring a pattern including both sharp and broad peaks since the effect of peak shape on the answer each gives i s unknown. In cases where the XRD pattern to be measured has a very large number of clo s e l y spaced peaks, a single invocation of CSP covering the entire target range of 26 was used. A 0.005°/s scanrate and a 5s counttime was used i f th i s 26 range was greater than 2 0 ° . The accuracy of these peak-seeking procedures, including the precision of standard peak measurement, i s 136 about ±0.01 °28 for MAX9, ±0.005°261 for CSP using the 0.002°/s scanrate and ±O.O2°20 for CSP using the 0.005°/s scanrat e. STANDARDS: Although the P h i l i p s goniometer i s precise to O.OO25°20, accurate measurements cannot be obtained by goniometer c a l i b r a t i o n alone. Geometric analysis of the goniometer dimensions shows that small variations in specimen height result in unacceptable systematic e r r o r s . For example, a change in specimen height of 0.1mm results in a systematic 28 error of 0 . 0 6 ° . The minerals used as internal standards were intimately mixed with the mineral being measured. The standards employed include Si metal, synthetic s p i n e l , synthetic p e r i c l a s e , and natural quartz (which had been ground, leached and annealed). SAMPLE MOUNTING: A l l samples were deposited from thick alcohol suspensions onto glass discs designed to f i t the P h i l i p s sample holders. In cases where preferred orientation was an undesireable tendency, the mineral powder was mixed with Buehler Transoptic powder which had been sieved to <50 nm. When deposited from a suspension, the mineral grains would adhere to the surface of the sp h e r i c a l , p l a s t i c Transoptic grains. 1 37 APPENDIX E: TRANSMITTED ELECTRON MICROSCOPY TEM l a t t i c e images are b a s i c a l l y interference patterns resulting from d i f f r a c t i o n of a p a r a l l e l beam of electrons as i t passes between regularly spaced planes of atoms. To obtain a s t r u c t u r a l l y interpretable TEM image the crystallographic planes of interest must be accurately oriented p a r a l l e l to the electron beam and a high magnification must be employed in order to resolve the interference pattern. The p r a c t i c a l requirements and factors to be considered in obtaining l a t t i c e images are as follows. THE ELECTRON MICROSCOPE'. The instrument must be physically and e l e c t r o n i c a l l y stable to prevent loss of resolution during photographic exposures of a few seconds. The instrument must be capable of routine application of magnifications greater than 200,000X. Smoothly operating, high tolerance stage motions, both linear and t i l t i n g , are desireable. THE SPECIMEN: Specimen grains must be thin enough to allow a majority of the beam to be transmitted through them. The grains must be separated from each other so that they can be studied i n d i v i d u a l l y . The physical support of the grains must be strong enough to be stable under the electron beam, and generally transparent to the electron beam. In addition, the 1 38 support f i l m should have holes in i t so that grains projecting over these holes can be studied without any foreign contributions to the image. THE BEAM: The electron beam should be small in diameter, free from astigmatism and accurately aligned along the axis of the instrument. Choosing an accelerating voltage requires consideration of the trade-off between brightness and contrast in the l a t t i c e image. A less energetic beam results in stronger contrast in the interference pattern. A more energetic beam has more penetrating power and so i t i s brighter and has a higher l i m i t of maximum specimen thickness. For d e t a i l s of the theory and p r a c t i c a l requirements of l a t t i c e imaging and review of i t s a p p l i c a t i o n s , useful references include Wenk et al(eds.,1976) and Spence(1981). ORTHOAMPHIBOLE LATTICE IMAGING The l a t t i c e imaging employed in characterizing the structure of synthetic orthoamphiboles was performed on a Hitachi H-800 STEM in the U.B.C. Metallurgy Department. The H-800 i s a d i g i t i z e d , microcomputer controlled instrument with a side-entry goniometer stage. It has a maximum accelerating potential of 200kV and a maximum magnification of 600,000 diameters. The crystallographic orientation of specimen grains i s f a c i l i t a t e d with a motor driven 1 39 d o u b l e - t i l t specimen holder having a maximum t i l t of ±45° on each a x i s . The instrument operating conditions generally used for l a t t i c e imaging are as follows: Accelerating potential 200kV Beam diameter 1 Mm Condenser aperture 300MITI Objective aperture 50 or 70MHI magnification 400,000X SPECIMEN MOUNTING: Synthetic amphibole grains were deposited from an alcohol suspension onto a holey carbon film which was supported by a 600mesh copper TEM support g r i d . Production of the holey carbon f i l m is begun by measuring into a v i a l , by volume, 5% c o l l o d i o n , 10% soapy water, and 85% amyl acetate. The v i a l i s sealed and agitated in a b a l l - m i l l shaker u n t i l the f l u i d appears uniformly milky white due to f i n e l y disseminated water and a i r bubbles. Several drops of th i s f l u i d are dropped into a container of water. Below the water surface in th i s container are several TEM support grids which s i t on a coarse wire screen. The film that forms on the water surface is allowed to 'dry' for a few minutes. The f i l m i s deposited onto the support grids by slowly draining the water out through the bottom of the container. After a l l remaining 1 40 water has dried from the screen, the TEM grids are removed and carbon coated. F i n a l l y the grids are c a r e f u l l y dipped into acetone for about 20 seconds each to remove the collodion f i l m ; leaving behind only the carbon coating. IMAGING PROCEDURES'. Each TEM session i s begun with beam and aperature alignment and fine tuning of beam astigmatism corrections. An amphibole bearing TEM grid i s loaded onto the d o u b l e - t i l t sample holder and inserted into the stage with a l l t i l t axes zeroed. Using low magnification bright f i e l d imaging, an appropriate grain i s sought. Several c r i t e r i a go into selection of an 'appropriate' grain; It must be thin enougn for l a t t i c e imaging (less than about 0.1 Mm (1000A) for Mg-Fe s i l i c a t e s ) . It must be s u f f i c i e n t l y s p a t i a l l y separated from other grains to allow independent observation of i t s electron d i f f r a c t i o n pattern. A portion of the grain must l i e in a position which i s r e l a t i v e l y close to the desired crystallographic o r i e n t a t i o n . Grains near the center of the mount are preferable since their s p a t i a l positions are least affected by the stage t i l t motions. The proportion of grains which can be oriented to a s p e c i f i c crystallographic d i r e c t i o n i s , in p r i n c i p l e , quite large since the t i l t motions of the stage have a t o t a l swing of 90° on each a x i s . In p r a c t i c e , i t was found that the t i l t motions were only p r a c t i c a l to ±20° above which stage d r i f t 141 became unacceptable for photography at high magnification. Orientation of orthoamphibole grains (mounted as described above) i s somewhat s i m p l i f i e d by their stucture and morphology. At zero stage t i l t the c-axis of most grains l i e s perpendicular to the electron beam. Due to the orthorhombic symmetry, the a and b axes of most grains then l i e in a plane p a r a l l e l to the beam. As a r e s u l t , the task of orienting grains with a or b axes p a r a l l e l to the beam is s i m p l i f i e d , and beam p a r a l l e l orientation of c-axes is impossible. Two dif f e r e n t stategies were used in searching for eas i l y orientable grains (a or b axes). One is a 'random walk' method. In this case the sample is slowly searched for grains already lying very close to the desired orientation by slowly scanning the grid with the instrument set in selected-area-diffraction mode. The second, and more systematic strategy is to search (bright f i e l d mode) for a grain which l i e s with i t s long axis nearly p a r a l l e l to one of the stage t i l t axes. Orientation of such a grain only requires motion on that one t i l t a x i s . Unfortunatly, the number of such grains which also s a t i s f i e d a l l of the other c r i t e r i a was found to be p a i n f u l l y few. The successful search for an 'appropriate' grain was often the most time-consuming step in obtaining each l a t t i c e image. Accurate crystallographic orientation i s accomplished by t i l t i n g the stage while observing the electron 142 d i f f r a c t i o n pattern of the target g r a i n . Frequent interruption of this process for re-centering and re-focussing the grain are i n e v i t a b l e . The electron d i f f r a c t i o n pattern i s b a s i c a l l y a zero-level reciprocal l a t t i c e image. The sp a t i a l pattern of d i f f r a c t i o n spots, for a major axis o r i e n t a t i o n , can eas i l y be predicted i f the space group and approximate unit c e l l repeats are already known. Proper crystallographic alignment i s recognized when the d i f f r a c t i o n spots have the appropriate s p a t i a l pattern and the d i s t r i b u t i o n of d i f f r a c t i o n i n t e n s i t i e s i s symmetric about the dir e c t beam spot. Once crystallographic orientation i s accomplished an objective aperature which passes about 20 d i f f r a c t e d beams is inserted. The instrument is returned to bright f i e l d mode and the magnification i s advanced to the highest p r a c t i c a l l e v e l . The image i s then accurately focused using the binocular (optical) microscope to magnify the fluorescent screen. If the l a t t i c e interference pattern i s not v i s i b l e at t h i s point, fine tuning of the beam astigmatism correction may be necessary. To prevent specimen contamination and structural damage (from the beam) prior to photography, the time spent focussing and adjusting stigmators should be minimized and/or these adjustments should be made with the beam on an area other than the area to be photographed. For each l a t t i c e image obtained, several photographs at s l i g h t l y d i f f e r e n t focus lev e l s and a 143 photographic record of the corresponding d i f f r a c t i o n pattern are d e s i r a b l e . The highest p r a c t i c a l l e v e l of magnification i s a function of image brightness and machine s t a b i l i t y . Physical and electronic d r i f t in the Hitachi H-800 was found to blur photographs taken with exposures longer than 5 seconds. The highest magnification at which the required photographic exposure was consistently less than 5 seconds was found to be 400,000X. 144 APPENDIX F: ORTHOAMPHIBOLE SYNTHESIS AND CHARACTERIZATION A series of orthoamphiboles in the system MgO-FeO-Si02_H20 have been synthesized for use as starting materials in ion-exchange equlibrium experiments. These ion-exchange experiments are designed to provide data for thermodynamic characterization of the Fe-Mg s o l i d solution in orthoamphiboles. The synthetic amphiboles were produced with hydrothermal techniques employing aqueous Fe-Mg chlorides as a f l u x . Both XRD and transmitted electron microscopy (TEM) techniques have been employed to characterize these synthetic products. The structural information gained with these techniques i s needed to f a c i l i t a t e comparison between the synthetic grains and natural anthophyllites. Previous studies have pointed out problems both with accomplishing high y i e l d syntheses and with comparison of synthetic orthoamphiboles with natural anthophyllites (Greenwood, 1963; Popp et a l , 1976). In general, hydrothermal treatment of oxide mixes within the orthoamphibole s t a b i l i t y f i e l d invariably results in production of s i g n i f i c a n t amounts of metastable t a l c , o l i v i n e , quartz ,±cristobalite, torthopyroxene. These metastable phases only slowly react to bring the amphibole y i e l d up to acceptable leve l s (2:99%). At compositions close to the Mg end-member creation of orthoamphibole nuclei has only been accomplished via breakdown of t a l c at (high) 1 45 temperatures outside the orthoamphibole s t a b i l i t y f i e l d . Popp et al(l976) concluded that their synthetic orthorhombic amphiboles possessed a structure unlike that of any known natural amphibole based upon discrepancies in unit c e l l volumes and upon a unique d i s t r i b u t i o n of i n t e n s i t i e s on electron d i f f r a c t i o n patterns. Subsequent HRTEM studies of these same synthetics by Veblen (as quoted by Gil b e r t et a l , 1982) revealed varying amounts of both chain-width and chain-stacking disorder (see also Veblen and Buseck, 1979). Synthetic Mn-Mg orthoamphiboles have also been found to contain chain-width and chain-stacking faults (Maresch and Czank, 1983). The use of an aqueous chloride flux in the present study was intended to: (1) promote reaction rates and minimize the time required for f u l l - y i e l d syntheses; (2) reduce the amount of chain-arrangement f a u l t s . Experimental Techniques STARTING MATERIALS'. A l l mixes were prepared from reagent grade S i 02 ( H2S i O „ • n H z O converted to c r i s t o b a l i t e at 1200°C), MgO, Fe203 and Fe (sponge). The equivalent of stoichiometric FeO was introduced as oxygen balanced proportions of Fe and Fe203. A l l oxides were thoroughly dried prior to weighing. Homogenization of the mixes was accomplished via a 1 46 combination of hand and automatic grinding in an agate mortar (under ethyl a l c o h o l ) . See Appendix A for additional d e t a i l s . The aqueous chloride flux consisted of reagent grade MgCl2-6H20 and FeCl2-4H20 dissolved in d i s t i l l e d water to a to t a l Mg+Fe concentration of Imolal. Solutions were prepared at XM g values of 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0. HYDROTHERMAL TECHNIQUES'. A l l runs were made in cold-seal type pressure vessels constructed of either s t e l l i t e 25 or Rene 41. Temperatures were measured with chromel-alumel thermocouples. Tight temperature control was not considered c r i t i c a l for syntheses, and the temperatures reported are only accurate to ±10°C. At 2kb, methane was used as the pressure medium in order to prevent oxidation of the charges via the graphite-methane buffer. At 4kb, the natural f~ of the bomb, using water as the pressure medium, was found to be s u f f i c i e n t l y low to prevent oxidation. Pressures were measured with bourdon-tube gauges. The reported pressures are accurate to ±120 bars. SYNTHESIS EXPERIMENTS'. Oxide mixes were prepared for amphibole compositions at XMg = 0.3, 0.5, 0.7, 0.9 and 1.0. For each experiment, c a r e f u l l y weighed amounts of oxide mix and aqueous f l u i d were sealed into a gold capsule. Composition changes in the 147 c r y s t a l l i n e charge bulk-composition had to be expected due to ion-exchange reaction with the aqueous chloride f l u x . Steps were taken to both control and measure these compositonal changes. Two methods were employed to control the effect of ion-exchange on the s i l i c a t e bulk-compositon. For each amphibole composition a chloride composition (XM g) could be chosen which was close to the equilibrium composition by using ion-exchange experiments with Fe-Mg o l i v i n e s as an example (see chapter I ) . The potential for compositional changes was further reduced by employing s o l i d : f l u i d ratios high enough to result in molar Mg+Fe ratios (sol i d : f l u i d ) between 20 and 50. Measurement of amphibole compositional changes was accomplished via measurement of Mg and Fe concentrations in the product aqueous f l u i d s . Subsequent c a l c u l a t i o n of the s i l i c a t e composition via mass balance i s quite accurate due to the combination of low weighing errors (generally less than 0.1%) and high Mg+Fe molar r a t i o s . After each run the capsule was cleaned with alcohol, cut open and i t s contents washed out in a known volume of a c i d i f i e d d i s t i l l e d water (0.03m in HN03). The s o l i d products were suspended and thoroughly washed with the help of an ultrasonic bath. The solids were then separated from the aqueous solution by cent r i f u g i n g . The supernatant aqueous solution was removed and analyzed for t o t a l Mg and Fe with standard flame atomic absorption techniques (see appendix B). The s o l i d products 1 48 are rewashed to remove any remaining traces of chlorides and dried at 120°C. By i n i t i a l l y washing the run products with a c i d i f i e d water, small amounts of non-silicate quench precipitates could be taken into s o l u t i o n . The resulting solutions were found to contain t o t a l Mg+Fe concentrations s i g n i f i c a n t l y in excess of that attributable to chlorides only for syntheses at 0.1 and 0.3 XM g ( s i l i c a t e bulk-composition). The synthesis strategy found most successful varied as a function of bulk composition. The 0.5 (XM g) mix composition was the only one which produced 99% y i e l d in one run. The 0.7 bulk composition reached a satisfactory y i e l d after one cycle of grinding and re-heating. Near the compositional extremes, the successful strategies were more elaborate. At the 0.9 and 1.0 bulk compositions the strategy employing ta l c formation followed by high temperature breakdown (Greenwood, 1963) was required to create amphibole n u c l e i . The desired results were only obtained when pure water was the only flux employed. The products of the nuclei-making cycle were reloaded with an aqueous chloride solution and re-run at a temperature low in the (Mg-rich) orthopyroxene+water s t a b i l i t y f i e l d . At higher temperatures, the rate of the metastable reaction: t a l c + f o r s t e r i t e = enstatite + H20 (in the presence of the chloride flux) was found to be so high that large, and therefore less reactive, grains of orthopyroxene quickly formed. 149 At 0.1 and 0.3 bulk compositions amphibole nuclei would form, but further progress of the synthesis was quite sluggish. The amphibole y i e l d was improved considerably by using seeded oxide mixes. The products of e a r l y , low y i e l d syntheses were ground and combined with oxide mix (same bulk composition) in a r a t i o between 2 and 5 (oxide:seed). . The d e t a i l s of the synthesis experiments are tabulated in table F1. UNIT CELL REFINEMENTS: Powder XRD techniques were employed to obtain unit c e l l parameters for every f i n a l sythesis product. The 26 data were obtained with a P h i l i p s PW1710 Automatic Powder DiffTactometer equipped with a graphite monochromator. D i g i t a l peak-seeking procedures were employed using Ni f i l t e r e d Cu r a d i a t i o n . Both synthetic p e r i c l a s e and natural quartz were used as internal standards. For technical d e t a i l s , see Appendix D. Least-squares refinement of the unit c e l l parameters was performed with the USGS FORTRAN IV program (Evans et a l , 1963). The results are l i s t e d in Table F2. Indexing of re f l e c t i o n s was done using the calculated anthophyllite powder pattern of Borg and Smith(l969) as a guide. One peak, common to a l l of the powder patterns and indexed as (400), i s not given any intensity at a l l by Borg and Smith. Popp et al(l976) and Maresch and Czank(l983) each found the same discrepancy when indexing powder patterns from their Table F1. Experimental parameters for orthoamphibole syntheses. The starting materials are an oxide mix (OX), the prodicts of a previous run (by run #) or a mixture of the two. The product phases are quartz (0), cristobalite (C), olivine (OL), orthopyroxene (OP), orthoamphibole (OA), and talc (TA). Product phases are listed in decreasing order of abundance with '+' meaning >1% and '-' meaning <1%. INITIAL FINAL STARTING SOLID FLUID FLUID SOLID PRODUCT RUN*1 MATERIAL Xu Xu mT T('C) P(kb) HOURS X„ X„ PHASES 214 OX 0 . 100 0 .000 1 .0 600 2 233 0 .050 0 .097 OL+C-OA 244 2 14+OX O .097 0 . 100 1 .0 600 4 172 0 .075 0 . 101 OA+OL+0 248 244 0 . 101 0 .000 1 .0 610 4 254 0 .048 0 . 100 OA+OL+0 260 248+OX 0 . 100 0 .000 1 .0 600 2 767 0 .029 0 . 104 OL+O+OA 304 260 0 . 104 0 .000 1 .0 500 2 432 0 .037 0 . 102 OA+0 207 OX 0 . 300 0 .000 2 .0 600 2 180 . 0 .079 0 . 297 OA+OL+Q 215 2O7+0X . O . 297 0 .300 1 .0 600 2 233 0 .082 0. . 339 OA-OL-C 188 OX 0. 500 0. . 300 1 .0 630 2 434 0. 127 0. 509 OA-OP 189 OX 0 700 0 300 1 .0 680 2 434 0. 243 0. 705 OA-OP 2 18 189 0. . 705 0. .500 1 .0 690 2 233 0. . 207 0. 753 OA-OP 258 OX 0. 900 •-- 0 .0 720 2 612 0. OOO 0. 900 TA+OA+OL 27 1 258 0. 900 0. 500 1 .0 665 2 279 0. 440 o. 903 OA+OL+TA 30O 27 1 0. 903 0: 500 1 .0 675 2 528 0. 443 0. 907 OA-0 315 OX 1 . 000 . . . 0 .0 700 2 183 0. 000 1. 000 TA+OA+OL+C 316 315 1 . 000 1. ooo 2 .0 675 2 481 1. OOO 1. 000 OA+TA+OL 317 316 1 . 000 1. 000 2 0 680 2 243 1. 000 1. 000 OA-TA o 151 Table F2. Orthoamphibole cell parameters derived from least squares refinement of powder XRO data. RUN* Mg a(A) b(A) c(A) V(A' ) * OF PEAKS 317 1 .OOO 18 .659(05) 17.920(05) 5 . 304(05 ) 1773.4(1.0) 1 1 300 0.907 18 . 579( 19) 17.975(39 ) 5 . 306(20) 1772.2(7.5) 9 218 0. 753 18 .685(05) 18.018(05) 5 .310(05) 1787.6(1 O) 12 188 0.509 18 .692(08) 18.136(18) 5. .325(25) 1805.3(8.0) 10 2 15 0 . 339 18 .682(07) 18.226(15) 5. .327(35) 1813.9110.) 9 304 0. 102 18 .705(05) 18.392(09) 5. .337(05) 1836 0(1.O) 1 1 In parentheses is one standard error of regression as applied to the last significant digit listed. synthetic orthoamphiboles. It is interesting to note that published powder patterns for natural a n t h o p h i l l i t e (Beatty, 1950), natural gedrite (Seki and Yamasaki, 1957; Milton and Ito, 1961) and synthetic gedrite (James et a l , 1976) a l l contain a peak which indexes as (400). D i f f i c u l t i e s were encountered in obtaining c e l l refinements for the products of runs 215 and 300. The powder pattern for each of these was unusually weak and in each case only a single weak peak could be indexed with a c component. This single peak had a grossly disproportionate influence on a and/or b in the c e l l refinement since i t was the only c-component peak and i t was not an (00/) peak. The c e l l parameters for these two synthetic compositions were obtained by removing the weak c-component peak and introducing a f i c t i t i o u s (002) r e f l e c t i o n into the c e l l 1 52 refinement.' The ^-spacing assigned to this r e f l e c t i o n was calculated by interpolating between c-repeats obtained for the remaining compositions. The a and b repeats calculated for these two synthetics are then influenced only by (hkO) r e f l e c t i o n s . The possible error introduced into c a l c u l a t i o n of the unit c e l l volume is probably very small since, as i l l u s t r a t e d below, the orthoamphibole c-repeat i s not strongly influenced by either Mg-Fe substitution or c r y s t a l l i z a t i o n conditions. The standard error (of regression) l i s t e d for runs 215 and 300 in table F2 is that calculated in the o r i g i n a l c a l c u l a t i o n which included only the weak c-component r e f l e c t i o n present in each powder pattern. The unit c e l l parameters l i s t e d in table F2 are presented graphically in figure F1. For comparison, c e l l parameters from the l i t e r a t u r e are plotted for synthetic Mg-orthoamphiboles (Greenwood, 1963, as indexed by Cameron, 1975; Chernosky et a l , 1984), synthetic Mg-Fe orthoamphiboles (Cameron, 1975; Ravior and Hinrichsen, 1975; Popp et a l , 1976) and natural anthophyllites low in components outside the FeO-MgO-Si02-H20 system (Johannson, 1930; Finger, 1970; S i e f e r t , 1977; Veblen and Burnham, 1978). The dashed straight l i n e s are the result of regression by Popp et al(l976) for their synthetic orthoamphiboles. The c-repeats of Mg-Fe orthoamphiboles from a l l sources are quite consistent. Neither Mg-Fe substitution nor 1 53 18.8 18.6-E o 18.4-co CD C 18.2 O 18.0-17.8 0.0 B- — — a-Repeat i " a b—Repeat C h sJ a C h • \ a p 0.2 0.4 0.6 0.8 X Mg 1.0 Figure F1. Orthoamphibole unit c e l l parameters. The f i l l e d symbols are data from the present study. Open symbols represent published values for other synthetic orthoamphiboles (Popp et a l , 1976; Ravior and Hinrichsen, 1975; Cameron, 1975; Chernosky et a l , submitted). Hatched symbols represent natural anthophyllites (Johannson, 1930; Finger, 1970; S e i f e r t , 1977; Veblen and Burnham, 1978). (a) The a and b repeats for orthoamphiboles plus Ch=chesterite (a and 2/56, Veblen and Burnham, 1978), J=jimthompsonite (a and 2/36, Veblen and Burnham, 1978), P=protoamphibole (2a and b, Gibbs, 1969), and C=cummingtonite (2asin/3 and b, Rice et a l , 1974). 1 54 5.6 CO E o i _ -*-> V) C7> C D 5.4 H c—Repeat 5.2 H Volume •1820 •1780 CO E o L_ - M CO cn c D 0.0 0.2 r~ 0.4 -1740 0.6 0.8 1.0 Figure F1. (b) -The c-repeat and unit c e l l volume. 1 55 c r y s t a l l i z a t i o n history appear to have much affect on this c e l l parameter. A small systematic discrepancy can be seen in the fc-repeats. Orthoamphiboles from the present study have 6-repeats generally s l i g h t l y lower than that of the natural anthophyllites and many other synthetics. The discrepancy amongst the synthetics seems to disappear near the extreme in Fe s u b s t i t u t i o n . A l l of the synthetic Fe-Mg orthoamphiboles have larger a-repeats than natural anthophyllites. The discrepancy is even greater for orthoamphiboles produced in the present study. Once again, the discrepancy amongst the synthetics disappears at low X^g. Minor element chemistry does not seem to be capable of accounting for the c e l l dimension discrepancies. Popp et al(!976) concluded that neither minor Al (in the natural examples) nor Fe-Mg s i t e ordering could account for c e l l volume discrepancies. Although Popp et a l directed their discussion toward contrasts in c e l l volume, figure F1 i l l u s t r a t e s that the c e l l volume discrepancy i s primarily due to the discrepancy in the a-repeat. Maresch and Czank(l983) have shown that Mn substitution expands the a-repeat more than Fe substitution does. Most of the natural examples in figure F1 contain less than 1mole% of Mn7Si8022(OH)2. Minor Cl-OH s o l i d solution must be considered as a p o s s i b i l i t y for amphiboles produced in the present study. However, the anomalously low a-repeat for the 1 56 product of run 300 seems to argue against this p o s s i b i l i t y . The most a t t r a c t i v e explanation for these unit c e l l discrepancies may be chain-arrangement order-disorder. Chain-width disorder in natural amphiboles has been i d e n t i f i e d by Veblen and Burnham(1979) with HRTEM imaging techniques. As stated above, HRTEM studies have found both chain-width fault s and chain-stacking f a u l t s in synthetic Mg-Fe orthoamphiboles and in synthetic Mn-Mg orthoamphiboles. For the Mg-Fe synthetics, chain-width faults were found (by Veblen) to be more common in the more magnesian examples and chain-stacking faul t s were found to be more common in the iron r i c h examples. The e f f e c t of chain-arrangement disorder on a powder XRD pattern would include a general broadening of the peaks and also a bias in peak p o s i t i o n . The size and d i r e c t i o n of this position bias w i l l depend on the structural dimensions of each type of fault and the population of each type. Additional peaks should not enter the pattern unless the 'disorder' includes volumetrically s i g n i f i c a n t ordered domains of these ' f a u l t s ' . The effect of chain-width disorder may be investigated by looking at the structural dimensions of ordered orthorhombic biopyriboles. The a-repeats and scaled ^-repeats for jimthompsonite ( t r i p l e chains) and chesterite (double and t r i p l e chains) are included in figure F1. The 6-repeats of these two structures are integral multiples of a s i l i c a t e chain-width and so each structure w i l l produce 157 powder XRD peaks at 26 angles comparable to those of orthoamphibole. The XRD bias produced by these two structures, as models of the chain-width f a u l t s , i s indicated by comparing the orthoamphibole fc-repeats with 2/3fc for j imthompsonite and 2/5/3 for c h e s t e r i t e . It appears that populations of t r i p l e - c h a i n f a u l t s in an amphibole w i l l tend to increase the apparent Z>-repeat and, to a lesser extent, increase the apparent a-repeat. Chain-stacking polymorphs which could be used a models for chain-stacking faults include cummingtonite (++++ stacking, see Thompson, 1981) and protoamphibole (+-+-stacking). The ++++ type of stacking fault does not appear capable of contributing to the observed discrepancies. The values of b and 2asin/3 for natural magnesian cummingtonite (Rice et a l , 1974; see figure F1) are e n t i r e l y consistent with b and a for natural anthophyllite. The values of b and 2a for the only known protoamphibole structure (Gibbs et a l , 1960; Gibbs, 1969) are also plotted on figure F1. The effect of the +-+- type of stacking f a u l t i s d i f f i c u l t to evaluate using t h i s example because the observable contrast in b and 2a may be largely due to the presence of L i in the M4 and A s i t e s . Comparison of the orthoenstatite and protoenstatite structures may help indicate at least the sign of an XRD bias produced by the +-+- type of stacking f a u l t . For pure Mg examples, a and b for orthoenstatite are 18.22A and 8.81A respectively and for protoenstatite 2a = 18.50A and b = 8.74A (Deer et a l , 1978). As with the i l l u s t r a t e d proto and 1 58 ortho amphibole examples, t h i s t r a n s i t i o n from ++-- stacking to +-+- stacking i s accompanied by a reduction in the chain-width dimension (b) and an expansion of the chain-stacking dimension (a). If chain-arrangement f a u l t s are c a l l e d upon to account for the observed c e l l dimension discrepancies and the models presented above are accepted as a q u a l i t a t i v e guide, then chain-stacking faults must be common in the synthetic orthoamphiboles produced in the present study. The exception is the products of run 300 which have a higher b and a lower a than the trends established by the remaining product amphiboles. The existence of these postulated stacking f a u l t s w i l l be investigated in the electron microscopy study which follows. ELECTRON MICROSCOPY: Transmitted electron microscopy was performed with an unmodified Hitachi H-800 200kV STEM equipped with a goniometer side-entry stage and d o u b l e - t i l t sample holder. Lat t i c e images were obtained at a primary magnification of 400,000X with a 70MIII objective aperature and a 200kV beam. Defocus values were generally 0 to -500A. Each amphibole sample was dispersed from an alcohol suspension onto a holey, carbon f i l m which was supported by a 600-mesh Cu g r i d . Additional technical d e t a i l s can be found in Appendix E. The low magnification b r i g h t - f i e l d images in plate 1 i l l u s t r a t e the morphology of the synthetic amphibole grains. 159 Plate 1. Low magnification bright f i e l d images of the synthetic orthoamphiboles. Each photograph i s marked with i t s corresponding run#. The scale bar applies to a l l of the photographs. IbO P l a t e 1 1 2 Lim 161 The more magnesian examples (produced at the highest temperatures) have the l a r g e s t g r a i n s i z e . The F e - r i c h s y n t h e t i c s not only have a smaller g r a i n s i z e , but a l s o a smaller length:width r a t i o . The photographed sample from run 317 had been ground i n a small b a l l m i l l to reduce g r a i n s i z e . The sample mounting method, although f a s t and t e c h n o l o g i c a l l y s i m p l e , proved to p l ace d e f i n i t e l i m i t s on the success of o b t a i n i n g s t r u c t u r a l i n f o r m a t i o n . P r e f e r r e d o r i e n t a t i o n produced by g r a i n morphology g e n e r a l l y r e s u l t e d in a high p o p u l a t i o n of o r i e n t a t i o n s near a-axis normal (O/c/), a lower p o p u l a t i o n of o r i e n t a t i o n s near 6-axis normal (hOl) and, of c ourse, a zero p o p u l a t i o n of o r i e n t a t i o n s near c-axis normal. S i m i l a r l y mounted s y n t h e t i c Mg-Mn orthoamphiboles have a l s o been found to have an a-normal p r e f e r r e d o r i e n t a t i o n (Maresch and Czank, 1983). In c o n t r a s t , the p r e f e r r e d o r i e n t a t i o n of the two most i r o n - r i c h s y n t h e t i c orthoamphiboles was found to be b i a s e d toward the fc-normal o r i e n t a t i o n . For the most magnesian c o m p o s i t i o n s , g r a i n s i z e proved to be a s e r i o u s l i m i t i n g f a c t o r . Only a small p o r t i o n of the g r a i n s mounted from runs 300 and 317 were t h i n enough f o r e l e c t r o n d i f f r a c t i o n and l a t t i c e imaging. Attempts to reduce g r a i n s i z e by .grinding succeeded only in reducing the l e n g t h of the g r a i n s . (Okl) Orientation: P l a t e 2 presents (Okl) l a t t i c e images 162 and corresponding electron d i f f r a c t i o n patterns for orthoamphibole grains from runs 188, 218 and 317. The various l i m i t s discussed above impeded successful l a t t i c e imaging of the remaining synthetics. Oriented electron d i f f r a c t i o n patterns were obtained for grains from runs 300 and 215. V i s i b l e chain-width fault s in the l a t t i c e images * and streaking of d i f f r a c t i o n spots along b indicate the presence of chain-width disorder. The population of chain-width fault s appears to be very low for the run 215 grain and r e l a t i v e l y high for the run 300 grain. For the other grains represented in plate 2, chain-width f a u l t s are generally present, but apparently a f f e c t i n g less than 10% of each grain volume. (hOl) Orientation-. Plate 3 presents {hOl) d i f f r a c t i o n patterns for a l l six synthetic compositions, plus a ( h O l ) l a t t i c e image for a grain from run 304. The streaking of * spots in the a d i r e c t i o n indicates that chain-stacking fa u l t s are common in a l l but the most i r o n - r i c h grains. In contrast to the powder XRD measurements of the a-repeat, the electron d i f f r a c t i o n pattern for the run 300 grain does not appear to be anomalous. DISCUSSION: If the few grains studied via TEM are compared with the powder XRD measurements, the explanation put forth for the discrepancies in c e l l dimensions i s supported. 1 63 Plate 2. High magnification images and electron d i f f r a c t i o n patterns for specimens in {Okl) o r i e n t a t i o n . Each photograph is marked with i t s corresponding run#. The =*9A spacing of the double-chain repeat serves as i t s own scale bar. A l l chain widths other than 2 are indicated. 1 65 Plate 3. Electron d i f f r a c t i o n patterns and one high magnification image for specimens in (AO/) o r i e n t a t i o n . The scale on the high magnification image i s i d e n t i c a l to that of Plate 2. 300 218 167 Chain-stacking disorder i s present in a l l but the most Fe-rich orthoamphiboles. Chain-width disorder i s detectable for most of the grains studied. The exception i s the sample from run 300 which, in contrast to the theory based upon XRD alone, appears to be anomalously high in chain-width disorder rather than anomalously low in chain-stacking disorder. This direct comparison of the powder XRD measurements and the information obtained in the TEM study is inconclusive since the TEM study sampled so few grains. For the magnesian orthoamphiboles, the TEM sampling i s also biased by i t s selection of the smallest grains. Further study i s s t i l l needed to conclusively i d e n t i f y the discrepancies between natural and synthetic orthoamphibole structures. 168 APPENDIX G: THE MG-FE ORTHOPYROXENE SOLUTION The data available from the l i t e r a t u r e which constrain the properties of the Fe-Mg orthopyroxene solution includes i n t r a c r y s t a l l i n e ion-exchange data, i n t e r c r y s t a l l i n e ion-exchange data, displaced oxidation equilibrium data and calorimetric data. The f i r s t of these data-types can be classed as microscopic while the l a t t e r three would be classed as macroscopic. Although orthopyroxene solution models have been proposed based upon the microscopic data alone (e.g. Saxena and Ghose, 1970, 1971; Navrotsky, 1971; Saxena, 1973), the internal ordering of Fe and Mg need not be the only contribution to the macroscopic thermodynamic behavior. A macroscopic solution-model need only consider the macroscopic data in order to interpolate between the data points. However, a microscopic model that i s consistent with both the macroscopic and microscopic data should provide more insight into the nature of the internal contributions to the macroscopic properties. For t h i s reason, a microscopic model should be more successful in extrapolation to both conditions and chemistries outside the o r i g i n a l data-set. In this appendix, a microscopic model i s applied to the Fe-Mg orthopyroxene solution after review and c r i t i q u e of the available microscopic and macroscopic data. INTRACRYSTALLINE I ON-EXCHANGE'. 169 The quantitative data for the temperature and compositional (x°Px) dependence of Mg-Fe ordering in orthopyroxene have a l l been derived from Mossbauer spectra of heated natural orthopyroxenes (Virgo and Hafner, 1969; Saxena and Ghose, 1971; Besancon, 1981 and submitted for publication; Besancon and Vaughan, submitted). Nearly a l l of these data consist of half-brackets from the low-temperature (more ordered) side. The exceptions are one ordering experiment by Virgo and Hafner and an ordering-rate study at 600°C by Besancon(submitted). Disordering rate studies by Virgo and Hafner(1969) and Besancon(1981) indicate that most of the half-brackets should adequately represent equilibrium. The exceptions are data at 500°C and 1000°C. Extrapolation by Besancon of his second-order rate equation down to 500°C indicated that the published 500°C heating experiments were not long enough to atta i n equilibrium. Extrapolation to 1000°C indicated that experiments at t h i s temperature could not be quenched fast enough to preserve the equilibrium state of disorder. Prior to application of the site-ordering data to c a l i b r a t i o n of a solution model, the accuracy of these data must be evaluated. The sources of error inherent in the site-ordering studies include: precision in measuring the Mossbauer spectra, r e p r o d u c i b i l i t y of the heating experiments, site-assignment for minor elements occupying octahedral s i t e s and uncertainty in the r a t i o between the M1 r e c o i l l e s s f r a c t i o n and the M2 r e c o i l l e s s f r a c t i o n . (The 170 57 r e c o i l l e s s fraction is the proportion of Fe atoms present that contribute to the measured gamma-ray absorption spectrum.) A l l of these w i l l be expressed here in terms of the natural logarithm of the d i s t r i b u t i o n c o e f f i c i e n t for Fe-Mg exchange between M1 and M2. _ Mg Mg , , D , 2" C c - < ' ) Mg Mg Precision estimates stated by the authors indicate that the error inherent in Mossbauer spectroscopy is t y p i c a l l y ±0.02 in l n KD 12 « Analysis of r e p l i c a t e heating experiments from Virgo and Hafner(l969) and Besancon(1981) indicates that the heating experiment r e p r o d u c i b i l i t y is approximately ±0.1 in l n KD 12 » Since the Mg d i s t r i b u t i o n determined in Mossbauer studies i s calculated by d i f f e r e n c e , small uncertainties in minor-element s i t e assignment and r e c o i l l e s s f r a c t i o n r a t i o translate into substantial errors in l n KD 1 2 for bulk compositions low in t o t a l Mg. A l l of the orthopyroxene s i t e d i s t r i b u t i o n studies mentioned above have assumed that the r e c o i l l e s s fraction r a t i o , Rrf/ i s unity. Virgo and Hafner(l968) state that R^^ = 1.0±0.1 based on the Mossbauer spectrum of synthetic o r t h o f e r r o s i l i t e . Virgo and Hafner(l969) state that the r e c o i l l e s s fractions for M1 and M2 are equal "within a few percent". Figure G1 shows the effect of a ±5% error in R ^ on s i t e d i s t r i b u t i o n s at lnKD 12 = -2.0 (when assuming R ^ = 1.0). 171 J I I • Spectroscopy I Heating Experiment Figure G1. Uncertainties inherent in measurement of orthopyroxene s i t e occupancies from Mossbauer spectra of the products of disordering experiments. 172 Minor occupants of the octahedral si t e s have been assumed to be i n s i g n i f i c a n t and simply ignored in the c a l c u l a t i o n of Mg s i t e d i s t r i b u t i o n s . This treatment e f f e c t i v e l y assumes that a l l of the minor elements are equally d i s t r i b u t e d between M1 and M2. Figure G1 also i l l u s t r a t e s the effect on l n KD 1 2 of a ±0.0latom error ( S i206 formula) in s i t e assignment (taking 0.01 atoms from one s i t e and re-assigning i t to the other s i t e ) . This i s equivalent to a 0.02atom error in chemical analysis for an element which would be ordered e n t i r e l y into a single s i t e . In l i g h t of the apparent importance of minor element s i t e assignment, a l l of the measured l n KD 1 2 values have been recalculated based on modern estimates of octahedral s i t e preference. Using the compilation of Cameron and Papike(l98l) as a guide, l n KD l 2 values were recalculated by placing Ca, Na, K and Mn e n t i r e l y in M2 and T i , Fe+ 3 and octahedral Al in M2. The results are l i s t e d in table G1 and i l l u s t r a t e d in figure G2. Notably absent from t h i s table and figure are the data for specimen #9 from Saxena and Ghose(l97l). Heating experiments on samples of this specimen (X°p x=0.86) were performed outside i t s s t a b i l i t y f i e l d with respect to o l i v i n e + quartz. Values of l n KD 1 2 measured for t h i s specimen are anomalously temperature independent and no p a r t i c u l a r attention was paid toward characterization of the products of these experiments. For these reasons, the data from specimen #9 are not included in the present study. 173 Table G1. Original and adjusted values of l n KD 12 . The references are: 1 = Virgo and Hafner(1969); 2 = Saxena and Ghose(l971); 3 = Besancon(1981); 4 = Besancon(submitted); 5 = Besancon and Vaughan(submitted). Reported Adjusted T(°C) XE n l n KD 1 2 l n KD 1 2 Ref. 500 0.819 -3.183 -3.294 500 0.619 -3.396 -3.392 500 0.545 -3.461 -3.660 500 0.500 -3.469 -3.682 500 0.420 -3.200 -3.644 500 0.380 -2.896 -3.360 500 0.280 -2.145 -2.646 600 0.819 -2.260 -2.350 600 0.619 -2.451 -2.453 600 0.545 -2.451 -2.595 600 0.500 -2.543 -2.692 600 0.420 -2.527 -2.828 600 0.380 -2.272 -2.589 600 0.280 -1.962 -2.412 600 0.240 -1.794 -2.494 700 0.819 -1.936 -2.024 700 0.619 -2.115 -2.111 700 0.545 -2.014 -2.151 700 0.420 -1.962 -2.187 700 0.380 -1.943 -2.204 800 0.819 -1.721 -1.806 800 0.619 -1.772 -1.769 800 0.545 -1.738 -1.868 800 0.500 -1.709 -1.829 800 0.380 -1.742 -1.979 800 0.280 -1.497 -1.842 174 Table G1. (continued) Reported Adjusted T(°C) XEn l n KD12 l n KD12 Ref . 1000 0.822 -1.405 -1.450 2 1 000 0.728 -1.422 -1.470 2 1 000 0.610 -1.403 -1.340 2 1 000 0.594 -1.648 -1.675 2 1 000 0.469 -1.525 -1.541 2 1000 0.426 -1.368 -1.402 2 1 000 0.369 -1.453 -1.649 2 1 000 0.302 -1.410 -1.406 2 1 000 0.239 -1.050 -1.048 2 1 000 0. 123 -0.645 -0.782 2 500 0.426 -2.864 -2.916 2 600 0.426 -1.936 -1.970 2 700 0.426 -1.772 -1.804 2 800 0.426 -1.518 -1.543 2 600 0.493 -2.121 -2.370 3 600 0.869 -1.706 -1.726 5 600 0.869 -1.801 -1.817 5 700 0.493 -1.780 -1.993 3 700 0.493 -2.116 -2.108 4 700 0.869 -1.319 -1.332 3 800 0.493 -1.444 -1.684 3 800 0.869 -1.003 -1.166 3 Review of figure G2 reveals d i s t i n c t discrepancies between the data sets from each of the three sources. The cause of these discrepancies i s not immediately evident from published accounts of the experiments. There are no basic differences in the procedures described in each study for 175 - 1 -- 2 -O - 3 -- 4 + + 1000°C v 800°C • 700°C o600°C A 500°C + + + v + + m V T • • • A A • 0.0 0.2 0.4 0.6 X En v • + o • o 0.8 1.0 Figure G2. Corrected l n KD 1 2 values plotted versus XE n» The f i l l e d symbols represent data from Saxena and Ghose(l970). The crosses and symbols containing a v e r t i c a l l i n e are from Virgo and Hafner(1969). The open symbols represent data from Besancon(1981), Besancon(submitted) and Besancon and Vaughan(submitted). 176 measurement and interpretation of the Mossbauer spectra. However, there are contrasts in the parameters of the heating experiments. Contrasts in experimental pressure appear to be ruled out as the source of l n KD 1 2 discrepancies. Duplicate heating experiments performed on samples of the same specimen at I8kb and I0~7bar by Virgo and Hafner resulted in indistinguishable values of l n KD l 2. Three d i f f e r e n t approaches have been used to prevent oxidation. These approaches are atmosphere control (H2-C02 gas mixing; Besancon, 1981), inert atmosphere (argon at 0.5 to 1.5kb; Saxena and Ghose, 1971) and lack of atmosphere (evacuated s i l i c a glass capsules; Virgo and Hafner, 1969). In a l l cases, experimental run products which showed evidence of oxidation were discarded. In conclusion, there seems to be no sound reason to discard any one data-set. The data set of Saxena and Ghose alone i s used in the present study because this data set i s the largest i n t e r n a l l y consistent set of data. It is proposed here that thermodynamic modelling of l n KD l 2 need not be asymmetric (with respect to X°p x) in order to s a t i s f y the Mossbauer data. Saxena and Ghose(l971) modelled the asymmetry in their data set with separate Margules excess functions for mixing on M1 and M2. It i s noted here that rejection of Saxena and Ghose's specimen #9 and r e d i s t r i b u t i o n of minor octahedral elements removes much of th i s asymmetry. The remaining amount of asymmetry is thrown into doubt by the uncertainty in R f and the 177 implications of Besancon's rate study on the 500°C data. It is worth noting here that Besancon(1981) found an order-of-magnitude difference between the disordering rates of his two specimens at x^ gX = 0.49 and 0.87. CALORIMETRY: Two calorimetric studies have compared enthalpies of solution of intermediate Mg-Fe orthopyroxenes. HF calorimetry at 73.5°C by Sahama and Torgeson(1949) was interpreted by the authors to be consistent with zero excess enthalpy of mixing. In f a c t , i t may not be possible to draw such conclusions from their data. Their study includes only 3 natural orthopyroxenes. Pure endmembers are not included, and no compositions between X°J^X= 0.27 and 0.96 are represented. A recent ( L i , N a ) B20 „ - m e l t solution calorimetry study by Chatillon-Colinet et al(l983) included 5 synthetic Mg-Fe orthopyroxenes that span the entire s o l i d s o l u t i o n . The authors interpreted their measurements at 750°C to be consistent with a symmetric Margules model with W°^x= 4kJ. ri The standard error in their individual calorimetric measurements indicates that this calculated WH i s precise to ±4kJ. Chatillon-Colinet et al(l983) interpret this Wu value to be that of pyroxenes having KD 1 2 values c h a r a c t e r i s t i c of equilibrium at 1120°C (the temperature of t h e i r synthesis). A recent ordering-rate study by Besancon and Vaughan(submitted for publication) shows that ordering rates are similar to disordering rates. This strongly suggests 178 that the synthetic orthopyroxenes had s u f f i c i e n t time to reach order-disorder equilibrium at the temperature of the calorimeter (750°C) prior to being dropped in to the borate melt. The resulting value of 4+4kJ for i s interpreted here as being c h a r a c t e r i s t i c of orthopyroxenes in order-disorder equilibrium at 750°C. OXIDATION EQUILIBRIA: Nafziger and Muan(l967), Kitayama and Katsura(1968) and Kitayama(1970) have studied the effect of Mg substitution on the reaction: FeSi03 = Fe + Si02 + 1/20Z (G2) Their approach was to vary P_ (oxygen p a r t i a l pressure was u2 assumed = f^. ) , at constant T, u n t i l metallic iron f i r s t u2 appeared in a sample which was i n i t i a l l y synthetic pyroxene or pyroxene + S i 02. The v a r i a t i o n of equilibrium p^ with XMg w a s u s e o- t o calculate an a-factor which i s proportional to the WG of a symmetric Margules formulation (WG=2.303RTa). The quoted a factors translate into Wg's ranging from 8kJ to 2kJ over the temperature range from 1150° to 1250°C (1atm). Unfortunately these experiments are of l i t t l e use in constraining the properties of the orthopyroxene sol u t i o n . A l l of the data in the studies l i s t e d above amount to half-brackets from the low p side of reaction (G2). No u2 1 79 attempts were made to establish reversals. The equilibrium XMgX w a s a s s u m ed t o D e that of the star t i n g material even though the method employed to detect reaction (G2) must change the composition of the pyroxene. An additional ambiguity in the a p p l i c a b i l i t y of these experiments stems from uncertainty in the structural state of the synthetic pyroxenes. Of the three experimental studies, only Kitayama and Katsura(1968) report structural i d e n t i f i c a t i o n of their pyroxenes. They concluded that their pyroxenes possessed the proto-pyroxene structure. INTERCRYSTALLINE ION-EXCHANGE: Measurements of Fe-Mg d i s t r i b u t i o n between orthopyroxene and other phases are represented in the l i t e r a t u r e by a large volume of natural mineral-pair examples plus experimental studies with o l i v i n e , Ca-rich pyroxene, garnet and cummingtonite (see Deer et a l , 1978, for review plus Sack, 1980; Fonarev. and Korolkov, 1980; Kawasaki and Matsui, 1983). Analysis of data from a single mineral pair can only compare the properties of the two phases. Absolute values of s o l i d solution properties can be estimated by simultaneously considering several (interdependent) ion-exchange e q u i l i b r i a plus any net-transfer equilibrium and calorimetric constraints on each of the solid-solutions involved and on each of the endmembers. Chapter II presents application of a comprehensive database for mineral data in the system 180 MgO-Si02-Fe-0-C-H (Engi et a l , 1984) to the analysis of ion-exchange e q u i l i b r i a with aqueous Mg-Fe chlorid e s . Remaining inconsistencies between the calculated thermodynamic model and orthopyroxene ion-exchange data (see Chapter II) point out the need for additional research. For the present, the orthopyroxene solution-model parameters l i s t e d under Model 2 in Chapter II (symmetric Margules formulation) are accepted as describing the macroscopic properties of t h i s s o l u t i o n . THE SOLUTION MODEL'. A speciation model (Greenwood and Brown, in preparation; Engi, 1983) i s chosen here for modelling the macroscopic and microscopic behavior of Mg-Fe orthopyroxenes. This model considers a mineral to be made up of additive structural units (as with Thompson, 1969; Kroger et a l 1959; Powell, 1983). These units are treated as d i s t i n c t molecular species whose concentrations depend on internal e q u i l i b r i a among the species, as constrained by mass-balance. The term 'speciation model' r e f l e c t s i t s s i m i l a r i t y to the di s t r i b u t i o n - o f - s p e c i e s problems t y p i c a l of modelling gaseous and aqueous sol u t i o n s . The structural units chosen for modelling the orthopyroxene are symmetrically equivalent units containing one each of the symmetrically d i s t i n c t octahedral s i t e s , M1 and M2. The four possible species, Mg(M1)Mg(M2)Si206, Mg(M1)Fe(M2)Si206, Fe(Ml)Mg(M2)Si206, and Fe(Ml)Fe(M2)Si206, 181 are a l l assumed to have d i s t i n c t free energies. The molar free energy of the o l i v i n e w i l l then depend on the concentration of these four species. Given an ov e r a l l mass-balance constraint, three of these concentrations are independent qu a n t i t i e s . Therefore the two compositional constraints, bulk composition and site-occupancy, are i n s u f f i c i e n t to determine a l l four concentrations. Calculation of a l l four concentrations requires consideration of 'mass action' constraints: the internal e q u i l i b r i a among the species. The following formulation is developed including non-ideal mixing of the species with each other as a p o s s i b i l i t y . The mass balance constraints, in terms of mole fr a c t i o n s , are: XMM + XMF + XFM + XFF = 1 ( G 3 ) where X ^ M g ( M 1 ) M g ( M 2) Si 206 a n d S O o n ? XE n + Xp s = 1 (G4) where X_ and X „ refer to the enstatite and f e r r o s i l i t e En Fs endmembers; XEn = XMM + ^ M F + 1/2 XFM ( G 5 ) 4 X.—, — X,-.,-, 1/2 X.,,-, Fs FF ' MF The internal e q u i l i b r i a Mg(M1)Fe(M2)Si 206 = + 1/2 XFM are: l/2Mg(M1)Mg(M2)Si206 + l/2Fe(M1)Fe(M2)Si206 K. ( XM MXF P)°'5 (W F F) 0 • 5 MF MF 'MF Fe(M1)Mg(M2)Si206 = 1/2Mg(M1)Mg(M2)Si206 + 1/2Fe(M1)Fe(M2)Si206 (X X )° '5( ' Y i ) 0 " 5 MM FF 7MM7FF FM = — FM 7FM The molar free energy of the s o l i d solution i s : GSS " XMMGEn+ XFFGFS+ XMFGMF+ XFMGFM " T Sc o n f + GS p e C EX where 183 Sconf = "R(XMMlnXMM+ XF Fl n XF F+ XMFl n XMF+ XFMl n XFM) ( G 1 2 ) and GgP e c is the excess free energy due to non-ideal mixing of the species. The stoichiometric 'bulk' excess free energy of t h i s model i s : GEXl k " GSS " GID ( G 1 3 ) where the free energy of the stoichiometric ideal solution i s : GID " XEnGEn + XF sGF s " T SI c o n f ( G 1 4 ) and the ideal configurational entropy i s : SIconf = -2 R ( XE nl n XE n + XF sl n XF s) ( G 1 5 ) Substituting (G11) and (G14) plus (G5) and (G6) into (G13) we have: ^ x " - X M F( GS F - ' /2^ n - 1 / 2 G F S > + XFM( GFM-,/2 GE ,T,''2 GFs) " T S E x " + G i f C < G , 6 » where 184 S ^l k = S , - ST f (G17) EX conf Iconf The expressions in parentheses in (G16) can be equated with the standard free energies of the internal e q u i l i b r i a : GEXl k = + XFM(-A G^ " T SEXl k + GEX8 C ( G 1 8 ) The numeric subscripts refer to equations (G7) and (G9). A second-order (symmetric) Margules formulation i s adopted here to describe the excess free energy of mixing the species. An expression for G|p e c was obtained by applying equation(8) of Berman and Brown(l984) and modifying the notation: GEX6 C = W1XMMXMF + W*XMMXFM + W 3XMFXFF + W«XF MXF F + W*XMFXFM + W«XM MXF F ( G 1 9 ) In an e f f o r t to reduce the number of f i t parameters, the excess energy of mixing the species i s modelled as being proportional to e l a s t i c l a t t i c e s t r a i n energy caused by volume mis-match between the species (Greenwood, 1979). The difference in volume between the MM and MF species i s assumed to be equal to the difference between the MF and FF species. The difference between the MM and FF species volumes i s assumed to be the sum of the MM-MF difference and the MF-FF difference. The volumes of the MF and FM are 185 assumed to be i d e n t i c a l . This la s t assumption forces the GEX6 C fu n c ti °n t o D e symmetric with respect to XE n. Combining a l l of these assumptions results i n : W, = W2 = W3 = W„ plus W5 = 0 and, because the re l a t i o n between displacement and e l a s t i c s t r a i n energy i s a 'square' law, W6 = 4W,. This reduces the number of Margules parameters to one, which w i l l be referred to as w^Pec (= W,). Rewriting (G19) in terms of W^ec and rearranging term: Qspec = W^e c( (X M M + X F P ) ( X M F + X F M ) + 4 X m m X F F ) (G20) Applying the general a c t i v i t y c o e f f i c i e n t expression of Berman and Brown(l984, equation (22)) results i n : RTln?MM = ^ " ^ F S + XF F} " GEXG C ( G 2 1 ) R T l n7 M p = R T l n7 p M = W ^ U ^ + Xp p) - G|P8 C (G22) R T l n7 F p = 2 W ^ ( XE n + X m m) - (G23) where GE^e c i s given by equation (G20). Before applying the above formulation, a method must be established for calculation of the species mole-fractions. If the mass-balance ((G3), (G4) and (G5)) and mass-action 186 ((G8) and (G10)) equations are combined and solved for a single mole-fraction, the result i s a quadratic in that mole f r a c t i o n . Solving for XM F results i n : 0 = X2F( ^ M F - b 2 ) + xM p b + XE n( XE n- D (G24) 7MM7FF where b - 1(, + b * M ) (G25) 2 KFM7FM Finding a solution for thi s quadratic i s an i t e r a t i v e process since the 7's depend on the values of the mole-fractions. I l l u s t r a t i o n of the relationship between the above formulation and measureable quantities i s f a c i l i t a t e d by rearrangement of the expressions for internal equilibrium, equations (G7) and (G9). The difference between these two equations i s the ion-exchange reaction that produces the long-range order measured in the Mossbauer studies. The standard free-energy of this exchange reaction w i l l be referred to as AGL (= AG °-AG 9). The sum of (G7) and (G9) describes the tendency toward short-range ordering: pairing or a n t i - p a i r i n g of l i k e octahedral ions. The standard free-energy of t h i s short-range ordering reaction w i l l be referred to as AGg (= A G 7 + A G 9 ) . This energetic drive toward short range ordering, AGg, is i d e n t i c a l to the AG^ or Bragg-Williams energy term used by Sack(l980) in his orthopyroxene model. Although 187 Sack(l980) stresses the importance of including t h i s term, he does not allow the reaction i t represents to proceed. In his basic formulation (see his equation (13)) the concentrations of the four 'endmembers' ( i d e n t i c a l to the four species considered here) are expressed only in terms of the site-occupancy numbers. This formulation can be shown to d i r e c t l y imply that A G° (AGg) = 0. Assignment of any other value to A G° is then inconsistent with his basic formulation. Comparison of the speciation model with the site-occupancy data i s accomplished by ca l c u l a t i n g lnKD 12 values with the help of the r e l a t i o n s : *Sg ' XMM + XMF ( G 2 6 ) XMg = XMM + XFM ( G 2 7 ) Comparison of the speciation model with the accepted macroscopic solution model i s accomplished through the r e l a t i o n : (G28) 188 The general properties of the speciation model can be estimated by reviewing equation (G18) with the understanding that variations in AG^ and AGg (and therefore variations in AG? and AGf) d i r e c t l y influence species abundances. If AG^ is either po s i t i v e or negative, i t s contribution to G ^ ^ i s negative. If AGg i s positive i t s contribution to G^"^ i s negative and vice versa. Any amount of ordering w i l l result in a small posit i v e contribution from the "TSgx^^ term. A positive WgPec translates d i r e c t l y into a positive contribution to G^ "'"'*. Figure G3 i l l u s t r a t e s the effect of speciation model parameters on lnKD 12 . A l l four curves were calculated with AGL = 15kJ. A positive AGg (anti-pair ordering) encourages long range ordering at intermediate bulk compositions. The opposite is true for a negative AGg (ion-pair ordering). A positive WgPec p r e f e r e n t i a l l y reduces the concentrations of the MM and FF species and encourages long-range ordering. Comparison with figure G2 shows that the site-occupancy data are consistent with a positive AGg and/or a positive Wg^ec. solution model (W^1''''1 function) developed in Chapter I I . This model i s characterized by a Gp^^ which is negative at Figure G4 includes a curve representing the macroscopic .bi G EX high temperatures and increases with decreasing temperature, Comparison of figures G2, G3 and G4 and review of the general properties of the above formulation reveals that manipulation of AGL and AGg values (holding WgPec=0) cannot simultaneously s a t i s f y both the macroscopic solution model 189 - 1 CN O - 3 -- 4 AGs(kJ) - 5 W* p e c (kJ) 0 0 " \ 0 5 AGL=15kJ T =600°C 0.0 0.2 r 0.4 0.6 0.8 1.0 Figure G3. LnKD 1 2 curves calculated from the speciation model formulation for sample values of AGr, A G „ , and W^pec, Li b (j A l l four curves were calculated at AG =15kJ and T=600°C. Li 190 and the l n KD 1 2 data. In p a r t i c u l a r , the increasing compositional dependence of l n KD 1 2 at low temperatures would require AGC to increase while the increase of G ^ i f ^ with decreasing T requires AGg to decrease. On the other hand, both of these trends in the data are consistent with both AG^ and WgPec increasing with decreasing temperature. Therefore, for this application of a speciation model to the available orthopyroxene data, AGg is assumed to be zero. The method employed in c a l i b r a t i n g the speciation model (as modified by assumptions described above) against the orthopyroxene data can be described as successive p a r t i a l regression. AGL was described by a two parameter function linear in temperature. WGpec was given a three parameter function characterized by a constant Wr . Pressure LP dependence was not included. The AG_ parameters were regressed to the l n KD 1 2 data while holding the WgPec parameters constant. Then the WgPec parameters were regressed to the macroscopic solution model while holding the (regressed) AGL parameters constant. The data points used in thi s second regression step were values of Gp"^ calculated from the macroscopic solution model at 50° intervals over the temperature range in which the macroscopic model i s constrained by data (550° to 1300°C). The computer program employed i s a 'derivative free' nonlinear regression program c a l l e d BMDPAR which is dis t r i b u t e d by BMDP S t a t i s t i c a l Software, Inc.. The two regression steps were repeated u n t i l each step revised the 191 regressed parameters by less than 0.2%. Some 'interval halving' was performed by hand to speed up the process. The resulting parameters are l i s t e d in table G2. DISCUSSION: The behavior of the speciation model described by the parameters in table G2 i s i l l u s t r a t e d in figures G4, G5, G6, G7, and G8. Figure G5 shows that the model f i t s the l n KD 1 2 data quite well considering the uncertainties which remain in the data s e t . Figure G4 shows that the WgU^ equivalent (calculated from (G28) at X_ =0.5) conforms to the tin macroscopic solution model over the temperature interval of the regression data. W^11^ conforms to the calorimetric data even though the model c a l i b r a t i o n was not constrained to do so. The steep plunge of W „u^ at high temperature i s a side effect of the constant WpPec formulation which does not allow WuPec to curve towards a constant value at high T. The rl steep plunge of W^0"^  and W^11"^  at low temperatures r e f l e c t s a t r a n s i t i o n into a region in which the Mg(M1)Fe(M2)Si206 species t o t a l l y dominates the s o l i d solution (see figure G7). Although WgPec continues to r i s e with f a l l i n g temperature (see figure G6), the species which WgPec most strongly a f f e c t s (MM and FF) become so rare that GgP e c plunges towards zero. Over this same t r a n s i t i o n region AGL and i t s negative contribution to G^"^ continue to r i s e . To summarize, the results of applying a speciation model to the orthopyroxene s o l i d solution imply that the 192 Table G2. F i t parameters resulting from successive p a r t i a l regression of the speciation model to the orthopyroxene data. 18820 (J/mole) 4.075 (j/mole/°C) spec H 43690 (J/mole) r,spec ws 58. 1 3 (J/mole/°C) wspec C -34.8 (j/mole/°C) macroscopic properties of th i s phase are the product of two opposing energies. The f i r s t of these i s the s t a b i l i z a t i o n energy gained from ordering two d i s t i n c t ions onto the two symmetrically and energetically d i s t i n c t octahedral s i t e s . The second is a d e s t a b i l i z a t i o n energy which i s modelled here as an e l a s t i c s t r a i n energy produced by constructing a continuous l a t t i c e out of structural units with s l i g h t l y d i f f e r i n g dimensions. As th i s s t r a i n energy increases with thermal contraction of the structure, the concentration of the units with the greatest volume contrast are reduced u n t i l f i n a l l y such units are v i r t u a l l y absent. If no s t a b i l i z a t i o n energy could be gained by ordering of Mg and Fe on the two s i t e s , then the macroscopic properties of the s o l i d solution would be dominated by the l a t t i c e strain energy; a positi v e 'excess' free energy. The o l i v i n e s o l i d solution seems to represent an example of this case. This Mg-Fe s o l i d solution i s characterized by l i t t l e 193 10000 6000-400 600 800 1000 1200 1400 1600 1800 Temperature (K) Figure G4. Comparison of macroscopic data, formulated as Margules parameters, with equivalents calculated at X,, =0.5 from the orthopyroxene speciation model. W p x (Model 2) refers to the macroscopic model developed in chapter I I . The' v e r t i c a l bar represents the calorimetric measurement of Chatillon-Colinet et a l ( l 9 8 3 ) . 1 94 -1 -- 2 -CN 5 - 3 -X En Figure G5. Comparison of lnKD 12 data from Saxena and Ghose(l970) with lnKD 12 curves calculated from the orthopyroxene speciation model. 1 95 400 600 800 1000 1200 1400 1600 1800 Temperature (K) Figure G6. GE X (equation (G18)) and i t s components calculated as a function of temperature for the orthopyroxene speciation model. 196 XMM X F F 400 600 800 1000 1200 1400 1600 1800 Temperature (K) Figure G7. Species concentrations calculated as a function of temperature at a constant X_=0.5 for the c a l i b r a t e d tin orthopyroxene speciation model. 1 97 1.0 X En Figure G8. Calculated t o t a l free energy of mixing for the orthopyroxene speciation model as a function of XE n. The value calculated i s GgS (equation (G11)) minus the f i r s t two terms of GI D (equation (G14)). 198 or no long range Mg-Fe ordering (see Brown, 1980 for review). The macroscopic excess free energy of the Mg-Fe o l i v i n e solution is positiv e (see chapters I and I I ) . Application of the implications of the orthopyroxene speciation model leads to the conclusion that the increase of w ° ll v i n e with decreasing temperature must produce some amount of ion anti-pair l o c a l ordering. SUGGESTIONS FOR FURTHER RESEARCH: The asymmetry in l n KD 1 2 with respect to bulk composition noted by Saxena and Ghose(l97l) may, in f a c t , be r e a l . If so, some of the assumptions used here to simplify the G!|pec function are inappropriate. Additional Mossbauer research aimed at confirming this asymmetry should attempt to remove the uncertainties which were noted above. The uncertainty in minor element s i t e assignment could be removed by studying synthetic orthopyroxenes. The uncertainty in the 500°C data set could be removed by repeating these experiments with durations consistent with exist i n g order-disorder rate studies. Consistent use of an f_ -buffered experimental environment may remove the inter-laboratory discrepancies found in the existi n g studies. The ambiguity that remains in applying the calorimetry of Chatillon-Colinet et al(l983) would not exist i f their study had included Mossbauer spectroscopy. Careful calorimetry at a lower temperature would have a greater 199 a b i l i t y to measure energetic contrasts between ordered and disordered pyroxenes. 

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